I think what the op is asking is more 3piece (as he calls park boots) and two piece (race boots).
Allthough worded wrong ring that is a fair enough question.
Op op a tradional 2 piece boot like most on the market will give the best all round performance in and out of the park. The downside can be the feel of the forward flex. It can sometimes be more harsh.
A three piece ice uses a differnt design where the flex comes from the tounge. They can offer a much nicer forward flex but in general will not ski as hardwood your out of the park quite a bit you may find you want somthing stiffer.
You ou can find just about any fit now from both styles so perhaps go to a boot fitter and try both styles and see what you prefer. Always take the boot fitters recommendations and remember you will need more then just the boot, footbeds of some time should be thought of as part of the boot not an extra.