- These alleged experts are no help.
- These so-called experts are no help.
Can anyone explain the difference?
Edited (because OP changed question):
Alleged, as an adjective, means that something was said to have taken place, but it has not been proven. It is often used when reporting about a person or incident that occurred, but the person has not yet been tried and convicted of the crime or the incident has not been verified by authorities. Unfortunately it is frequently used incorrectly. In your first example sentence, alleged means "asserted to be true, often without or before proof."
A usage note from the American Heritage Dictionary entry on using alleged as an adjective says:
So-called doesn't have the legal weight the term alleged has. In the context of your example, it means that what follows is "incorrectly or falsely termed" or that the speaker or writer doubts the truth of the following term. For example: The so-called experts did not know anything that could help me. So-called also has a definition of "commonly called", but I believe it is more often used to cast doubt on the term that follows.
A usage note from the American Heritage Dictionary entry for so-called says:
Alleged can always be used in place of so-called, though the latter is less formal.
So-called cannot however, always be substituted for alleged for 3 reasons:
1) As noted in the comments, alleged can also be used as a verb. So-called is always an adjective.
2) The aforementioned question of formality.
3) in some specific, formal, legal contexts, alleged carries special meaning with regard to accusations of criminal intent this is true because of the presumption of innocence under which many courts operate.