I work at a fairly small gym, and I'd much rather coach at a small gym than a large one.
Also, having seen how the owner and the coaches handle things, I'd probably rather be a parent at a small gym than a large one. The reason is that if you have a question, a complaint, a concern, anything, the owner is far more likely to listen and take you seriously at a small gym, simply because each person is a larger chunk of the clientelle. Almost any time a parent comes to my gym's owner with a complaint or a concern, she brings it up specifically at the next coaches' meeting so we can discuss how to address it. And sometimes, sure, we reach the conclusion that we should ignore the complaint, but the fact is that we always discuss it. I suspect this would not be the case at a large gym, where each kid represents a much smaller portion of the gym's business.
That said, Mac is indeed correct in saying that the philosophy of a gym is far more important than the size.
I would like to comment, however on what he was saying about how experienced the coaches are; often coaches who haven't been doing it as long are more enthusiastic, and thus more effective, than those who have been doing it for several decades.
The single worst coach I know of has been coaching for around 20 years. Having long since convinced herself that she knows everything, she has effectively made herself unable to learn anything new about the sport for many years, and that (among other things) has made her extremely inneffective as a coach.
Compare that with one of the coaches I work with now, who was never a gymnast and has only been coaching for four years. I consider him to be among the best coaches in the state.
To be sure, a brand new coach will not be as effective as one who has been coaching for a couple of years, but I have seen nothing that suggests to me that coaches with 15 or more years of experience are universally better than coaches with three or four years of experience.