It depends on the species.
It's basically a trade off between filter size and beneficial bacteria, how often and how much you want to do water changes, and how much tank space you have. Bigger is better because you can do less frequent water changes in the beginning and toward the end you won't have to keep pulling some and sticking in other tanks, or doing daily water changes.
In the past six months I've used between a 5.5 and a 20 gallon for growing out fry, and had definitely better results with more room, but the majority have been in a 10g because that's what I had most space for at the time. And the fry seem to do OK up to an inch, but then I'm mostly doing CA cichlids which are not as sensitive to water quality as say angelfish or something like that, and I'm doing water changes every few days or even every other day to keep the bottom clean (just a sponge filter) and to keep nitrates down.
Overfiltration and larger tanks are better if you can make room, have the money, and have the patience not to stick something else in the 'fry growout' tank.
