[susan53]

I talked above about the use of will/would to express volition. The other use is prediction.
Eg: John'll be lying on the beach at the moment makes a prediction about a present event (John lying on the beach); I'll see you tomorrow makes a prediction of a future event (seeing the person tomorrow); Mary will have arrived by now makes a prediction of a past (Mary having already arrived).

As I said before the second form of the verb makes it more "distant" - ie less direct psychologically - and therefore more polite. It's used in contexts where it's necessary to "save face"

So the literal meaning of both is "I predict my happiness if I help you", with would making it less direct in tone than will.

However here,
a) the literal meaning is largely irrelevant : the phrase is a conventional acceptance formula
b) As it expresses a concept that's going to be pleasing to the listener in any case, the use of the less direct form would isn't essential in terms of saving face. Again, it's just a conventional formula.

So in the context of using the phrase to accept a request there's no difference in the effect on the listener at all - the two are interchangeable.