Theres basically two extremes of body positioning in cycling, track sprinter position at one extreme and TT position at the other, with road and crit in the middle, with crit closer to the track sprinter position.

Track sprinters tend to have the bars closer to their hips, not as laid out as road riders, which gives more mechanical advantage when sprinting out of the saddle. They also tend to have more bend in the knee which gives a smoother high cadence spin.

I wouldn't change my position based on a road race v. crit, but since I race only crits, I have a shorter stem and a little more knee bend than a lot of guys would who only road race.