[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.

[fface]

Quote susan53

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"

Hi susan,

Could you please tell me how to use 'would' in a context where it's necessary to "save face"?

Thanks again!

[susan53]

Any time when what is said is potentially a cause of embarrassment for the listener. Eg a request, where they might be "pushed" into having to refuse. Small requests are less likely to be refused and therefore don't need such "careful" handling :
A : Brian, can you lend me €2 ? I want to get a coffee from the machine and I don't have any coins.
The same is true of the refusal:
B: Sorry, neither do I. Try asking John.
Neither person is "threatened" by either the request or the refusal and both can be made directly without either person losing face.

But "large" requests are tricky, and the request/reply forms have to become correspondingly more tentative:

A : Brian I'm sorry but I have a big favour to ask. The thing is... (= pre-request sequence "warns" the listener that a problematic request is coming, which allows them to mentally prepare)
.... I've got to pay my rent tomorrow and I don't have any money left. (Explanation of situation - again "prepares" the listener for what's coming)
Would you mind awfully lending me €500 till Friday when I get paid? (Request phrased much more tentatively, by asking about the listeners hypothetical displeasure at the idea of the request)
B : I'm really sorry Anne... (extended apology to warn the listener of the coming refusal and "soften" it)
... I would love to help but... (expression of hypothetical willingness followed by "but", again to warn the listener that a refusal is coming and to "soften" it.)
I'm afraid that ... (another apology =more warning and "softening")
I can't. (the refusal itself)
I don't have the money (Explanation to justify the refusal and emphasise that it's not a personal rejection)

Compare that with the following - which would be much more "threatening" to both parties :
A : Brian, can you lend me €500?
B : No.