I am neither a shaper nor a park-rider, but found the question interesting somehow, even though, like Phil pointed out, it is not very clear to start with..
This is why I came up with the no-sidecut board picture of Bruce Varsava from Coiler, to stir up discussion. If it turns up in an argument, I'll just look somewhere else.
Now my 2 cents:
As far as shape for park boards is concerned, I would say, from my experience in the park in both skateboard and rollerskates, that the sidecut length must act a little bit like the flex in the trucks (either by tightening/loosening thm or by varying the flex of the silentblocks). So, from there, I would say that the longer the sidecut the less forgiving the board would be, but mith more performance.
Having said that, it seems to me that most of the shape evolution for freestyle boards has not been on this parameter and rather on rocker (like the skate-banana) or flex of boards. There must be a reason.
One option could be to have a board with no sidecut or a very long one and a slightly concave base, which would cover reception/turn initiation needs. But I guess it would be detrimental to speed, hence to overall performance.