I guess I think it's about perspective. Where does the pressure come from? Are we talking about pressure to win, pressure to "prove" yourself, etc? When it comes down to it, big gym vs. little gym is all about strategy. Our gym is a small gym, and I can't help but reiterate some of the things above posters have said. If I make level appropriate teams (even if they're small teams), coach them well, and define our success appropriately***(more below) then my teams carry a lot less pressure on their shoulders, perform more confidently, and in turn are happier and want to stay with us rather than seeing if the grass is greener at the big gym up the road. What's better than that?
***As far as defining success, I tend to take a lot of issue with winning as a measure of success. Winning is not the goal. It's a perk of a job well done. I define our success as clean, deduction-free routines. When we do that, we do that we score well and our kids feel accomplished. We've stopped competing against other gyms (you will never hear my teams say, "Oh we just HAVE TO beat ABC All-Stars"), and we compete against ourselves. They are challenged to hit their routine cleanly, and then the placement is just the icing on the cake. Everyone loves winning, but my kids understand that a deduction free routine is the goal.