The biggest difference between the two forms—and one so obvious that neither of the earlier two answers points it out—is that proved is used in the simple past tense, whereas proven is not:
Euclid proved [not proven] the proposition with remarkable economy and rigor.
Another big difference involves the historical status of the two words: For much of the time since 1750, proven was far less common than proved as a past participle in published works. Here is an Ngram chart plotting instances of "has been proved" (blue line) against instances of "has been proven" (red line) in a Google Books search across the years 1750–2005:
And here is an Ngram chart of "have been proved" (blue line) matched with "have been proven" (red line) over the same period:
In both instances, what had been a very large advantage for "been proved" over "been proven" has melted away—and it bears emphasizing that the results shown here are from (in most cases) copyedited and professionally published writing—not from spoken English.
'Proved' versus 'Proven' Through the Years
Why was "been proved" so much more popular than "been proven" for so long? Its original advantage presumably reflected the preferences then current in spoken English. But starting in the early 1800s, as style and usage guides (and dictionaries) began to proliferate, these authorities began insisting on the rightness of proved and the wrongness of proven.
One early discussion of popular use of proven in North America occurs in John Pickering, A Vocabulary, or Collection of Words and Phrases Which Have Been Supposed to Be Peculiar to the United States of America (1816):
PROVEN for PROVED.
This is often heard in the debates of Congress, and is sometimes used by writers in the Southern States ; but it is unknown in New England. "There is (says an English friend) much affectation in the use of the words proven and stricken among certain American writers and speakers. To labour, as some do, to raise old words from the dead, is not only not tanti ; but it shews, that the persons who use these exertions do not consider, that if they are in any degree proper, they ought to be carried out to a much greater extent than the parties seem to be aware of."
But soon enough the usage ceases to be viewed as a charming provincialism and instead receives condemnation as an error. From Joseph Hull, *Appendix to Lectures on English Grammar* (1828), in the section headed "Vulgarisms":
Learnt for learned, and proven for proved, are common errors.
Seth Hurd, A Grammatical Corrector (1845) strikes a somewhat conciliatory note, listing proven in his section on "Optional Words and Phrases" about which he says, "Being however, somewhat less objectionable than those constituting the body of the work, they have not, like them, been absolutely condemned by the author":
PROVEN, for proved; as "His guilt was clearly proven."
And Richard Bache, Vulgarisms & Other Errors of Speech, second edition (1869), in a chapter titled "Obsolete, Obsolescent, and Local," has this:
Proven for Proved. Proven does not enjoy the wide use and sanction of good speakers, that should entitle it to take precedence of proved. It is used chiefly in Scotland.
In prose nearly obsolete, but retained by the poets : "When hearts whose truth was proven."—Waller
Standing against this tide of opinion is Thomas Lounsbury, History of the English Language (1879):
One marked form is, however, here to be noticed : this is the past participle proven for proved. The word is derived from the French, and in literary use has been inflected, until the present century, like all other foreign verbs, according to the weak conjugation throughout. But the strong participial form proven has made its way from the Scottish sub-dialect of the Northern dialect into the language of literature, and not only has grown common, but promises to become universal ; for it is employed by many of the best modern writers, and in particular, occurs frequently in the later poems of Tennyson.
But Luther Townsend, The Art of Speech (1881) counters by including "Proven, for proved" in a list of "provincialisms [that] should not be allowed to mar the sentences of any one who aims at correct and chaste speech."
William Hills, The Writer (November 1908) treats using proven for proved as an ill-informed attempt at genteelism:
The misuse of "dove" for "dived," and "proven" for "proved," and "had drank" for "had drunk" is especially common among people who are particular about their language, and who are always careful to say "between you and I."
Frank Vizetelly, A Desk-Book of Errors in English (1908) concedes a very narrow area of acceptable usage to proven:
proven : An irregular form of the past participle of prove used correctly only in courts of law. The word should be restricted to the Scotch verdict of "not proven," which signifies of a charge that it has neither been proved nor disproved. The modern pernicious tendency among reporters is to use proven instead of proved.
But Sherwin Cody, Standard Test English (1920) objects to proven on very different grounds:
Avoid proven for proved, as it is antiquated. Say, He hasn't proved his claim (not "proven his claim").
So, on the one hand (Vizetelly's), usage of proven is a modern pernicious tendency among reporters; and on the other (Cody's), it is antiquated.
H. W. Fowler, A Dictionary of Modern English Usage (1926) has this advice:
Except in the phrase not proven as a quotation from Scotch law, proven is better left alone.
More-Recent Views of 'Proved' versus 'Proven'
Bergan Evans & Cornelia Evans, A Dictionary of Contemporary American Usage (1957) try to focus on how proved and proven were actually being used in 1957:
prove. The past tense is proved. The participle is proven or proved. The participle proven is respectable literary English. In the United States it is used more often than the form proved. In Great Britain proved is used more often and proven sounds affected to many people.
And Webster's Dictionary of English Usage (1989) offers these remarks:
proved, proven A lot of ink has been devoted to questioning the propriety of proven versus proved since the controversy started in the 19th century (our earliest comment comes from 1829). ...
Surveys thirty or forty years ago showed proved to be about four times as common as proven. But proven has caught up in the past twenty years; it is now just about as common as proved as part of a verb phrase; it is more common than proved when used as an attributive adjective. You can use whichever form you like.
However, Roy Copperud, American Usage and Style: The Consensus (1980) sounds a more cautious note:
proved, proven. Four critics [including Theodore Bernstein, The Careful Writer (1965) and Wilson Follett, Modern American Usage (1966)] and American Heritage [Dictionary] object to proven as the past participle of prove: "The mine has proven worthless." Three others consider proved and proven equally acceptable, and both Random House [Dictionary] and [Merriam-]Webster regard proven as standard. Opinion is thus divided.
There is reason to suspect that those who declare for proved are taking their cue from Britain. ... Haggling over the propriety of proven vs. proved in a language like English, which is nothing if not irregular, is surely unreasonable.
William Morris & Mary Morris, Harper Dictionary of Contemporary Usage (1985) comes out generally in favor of proven:
proved/proven Proven, as the past participle of the verb "prove," is not recognized by some linguists. They insist that the past participle is proved only.
...
Many Americans have shown a preference for proven, as in "He has proven to be a valuable worker," and most current dictionaries list proven as having equal rank with proved, especially when used as an attributive adjective: a proven success.
And Kenneth Wilson, The Columbia Guide to Standard American English (1993) has this:
prove (v.) The principal parts are prove, proved, and proved or proven. Both proved and proven are used not only as past participles but also as participial adjectives [examples omitted]. Generally, proved is much more frequent as participle, proven more frequent as attributive adjective.
Nevertheless, a couple of high-profile holdouts remain. From Allan Siegal & William G. Connolly, The New York Times Manual of Style and Usage (1999):
proved, proven. In general proved is preferred: The prosecutor had proved the defendant's guilt. But as an adjective before a noun, proven is better: a proven remedy, proven oil reserves.
And from Bryan Garner, Garner's Modern American Usage, third edition (2009):
proved; proven Proved has long been the preferred past participle of prove. But proven often ill-advisedly appears [examples omitted].
In AmE, proven, like stricken, properly exists only as an adjective [examples omitted].
Proven has survived as a past participle in legal usage in two phrases: first, in the phrase innocent until proven guilty; second in the verdict Not proven, a jury answer no longer widely used except in Scots law. As for Not proven, one writer had defined this verdict as meaning, "Not guilty, but don't do it again."
Realistically, considering that published instances of "have been proven" are approximately equal to instances of "have been proved," Garner's notion that proven properly exists only as an adjective seems very difficult to sustain. On the other hand, I'm rather astonished that Mark Mussari, The Sonnets (2010) finds it necessary to translate Shakespeare's use of proved (to proven) so that a modern audience will recognize what the bard meant to say:
The speaker closes this sonnet with legal language: "If this be error, and upon me proved, / I never writ, nor no man ever loved." The speaker argues that everything he has said must be proven ("proved") to be an error.
'Proved' versus 'Proven' as Adjectives
As for proven versus proved as an adjective, here is an Ngram chart for "a proved" (blue line) versus "a proven" (red line) for the years 1750–2005:
The triumph of "a proven" since about 1960 could hardly be more complete.
Concluding Remarks
It may seem silly to worry about using "has been proven" today, when as many people use that formulation in edited publications as use "has been proved." But it's worth observing that some readers continue to view proven as a mistake in that situation,—which may or may not matter to you. Once you know the history of the dispute, you can proceed with your eyes open and make an informed decision about which word suits your purpose and your preferences better.