I think in general (there are always exceptions), the later it is the easier the transition. My DS is/was 98th percentile and we moved him around two years because I thought he 'looked too big' and it was not easy. It got better only when we put a gate at his door so he could no longer come out constantly (it was like a compulsion and worse the more tired he was. My DD is/was also 98th percentile. At 2.5 we took one side off her crib so she can get in and out. At 3.5 she has only just this week TRULY become too big for the crib and is now on a mattress on the floor until her new big girl bed arrives next week.
So my advice is, if he's sleeping well, don't rock the boat. Of course if he starts climbing out, then it's a safety issue and he needs to go in a big boy bed.