Powerlifting "type" of training should not make u slow.... Unless your REALLY TRYInG TO LIFT HEAVY! Witch would be the point of powerlifting. If your doin as you say powerlifting "style" then u might as well do oly lifting (for form) or just go cross fit. As if you have not noticed that's what cross-fit is. Just with much lighter weight.
So for you to say you can powerlift and not get slow, is not smart. If a weight being moved is heavy it will move slow........
That is just plain wrong. It will not make you slow. This is a complete misnomer. Lifting very heavy weights, even slowly, will never make you slow. The only reason the heavy weight is moving slow is because you can't possibly produce enough force to move it quickly. When you are talking about moving submaximal loads, things change.
Think of it like this. If you take two people: one who can deadlift a 1RM of 500 pounds and one who can deadlift a 1RM of 700 pounds, who would you guess is capable of moving 400 pounds at a higher velocity? My vote is going to person B. By increasing maximal strength, you decrease the intensity of moving submaximal external loads.
Granted, what I have just stated applies less when we're talking about very submaximal weights, such as your bodyweight or a very light implement like a ball. However, the same still applies to some extent. By increasing maximal strength it doesn't much affect the maximal velocity at which you are capable of moving/accelerating a limb. It does, however, improve the velocity at which you can move that limb if it is loaded in an significant fashion. In some cases, this does apply to bodyweight, especially when we're talking about the full load of your bodyweight being manipulated by a single limb (Which happens plenty in most athletic endeavors).
Improving maximal strength will help more in some sports than others. Football and wrestling are two examples where it can help quite a lot. However, it will NEVER, I repeat, NEVER, make you slower.