Both of the sentences sound a little weird to me, I think it is the "good as the best" part. Or maybe it is my confusion on how, empirically, would you compare yourself cross-generationally?
That aside though, I don't think there's a remarkable difference between "best of any generation" and "best of all generations."
EDIT: @Mitsu4u is correct in that the meaning of the sentence changes with the use of all; its meaning implies that you would be comparing yourself to the best person since the beginning of time.
A more natural-sounding phrase overall might be:
All I ask is a chance to prove that my worth matches that of the best of any generation.