We sometimes see both cases, such as "the famous church" and "the famed church". In what situation or objective do you use "famous" and "famed"? Please advise.
"much talked about," 1530s, past participle adjective from fame "spread abroad, report" (v.), c. 1300, from Old French famer, from fame "reputation, renown" (see fame (n.)).
As you can see, since famed derives from a past participle, its usage is more specialized than famous, as famed is best used for historical places, events, old/deceased people who were once famous. It's used to give respect to past accomplishments. On the other hand, famous is a more versatile option because it can be used to describe both past and present fame, however it is best served when describing a presently famous thing.
late 14c., "celebrated in public report, renowned, well-known" also "notorious, infamous," from Anglo-French famous, Old French fameus (Modern French fameux), from Latin famosus "much talked of, renowned," often "infamous, notorious, of ill repute," from fama (see fame (n.)).
As you can see, "celebrated in public report" suggests that the subject in question is presently famous.
Usage in literature:
Devon, Its Moorlands, Streams and Coasts by Rosalind Northcote
"Tiverton was famed in early days for its trade in wool."
Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 6 by Various
"The author at once became famous, although he had not, even yet, completed his fifteenth year."
As you can see here, famed wouldn't work in the second sentence, but famous would work in both sentences, albeit famed is better suited in the first because of its past-tense-niche nature.
Another difference is that famed sometimes indicates a smaller degree of fame than famous does. For instance, if someone in a niche field who was only recognized within that field were to die, you wouldn't describe him as famous, but famed. It's more respectful.
A simple Google search of the term ' "famed" dies ' shows that the word famous wouldn't be a good substitute for this specific case. 99% of these people the average person has no clue of, so famed is a nice alternative to pay respect while not commiting hyperbole.
Bill Cunningham, Famed Street Fashion Photographer, Dies At 87
Kimbo Slice, Famed Mixed Martial Artist, Dies in Florida at 42
Famed Cancer Theorist Dr. Alfred G. Knudson Jr. Dies at 93
Frank Lloyd Wright Dies; Famed Architect Was 89
'Future Shock' author and famed futurist Alvin Toffler dies at 87
Famed river guide George Wendt dies at 74
Famed Pakistan philanthropist Edhi dies in Karachi
Steve Pisanos Dies at 96: Famed Decorated WWII Fighter Pilot
Vic Kleman, famed Kennywood coaster enthusiast, dies at 83
In summary, you wouldn't use famed for something that became instantly famous, as evidenced by this Ngram:
Google search for "instantly famous": 47,800 results
Google search for "instantly famed": 387 results
Famed is a synonym of famous. The difference between famed and famous is that famed is having fame; famous or noted while famous is well known.
Sydney is famous/famed for its opera house