Generally I brew when I want, and if there's a competition that arises and I have something ready to submit, I'll enter it. So I am not exactly the "brew for a competition" type.
That said, something that is scheduled and for which you'd really want to participate, like your own homebrew club's internal competition, I understand the reasoning. I think my club is doing a brew-off against another club late this year so I'll be brewing specifically for that one.
The short answer is that there is no clear answer. It all depends on the styles you are brewing, scheduling them so they're at the optimal age.
The longer answer, however, is for most beers that you'd probably err towards fresher rather than not. Anything that requires strong hop aroma should be as fresh as you can do. Anything that is very low gravity tends to prefer freshness. Beers that are more neutral, higher ABV, and won't fade can go a bit longer. This of course takes into account the assumption that if all your processes are good, freshness is better. I'm not a big believer that beers "need" to age to taste good, because I know that I can go grain to glass in under two weeks on some beers and they're great.
So the key is to plan out exactly what you want to brew. Figure out what ages better or worse, and plan your brew days accordingly such that the beers that need to be freshest are the last ones to brew. And obviously if you're brewing something that really appreciates age, you want to brew those as far in advance as possible.