I'm not a big trem user, but I believe the modern 2-point trem is meant to be more responsive and hold its tuning better than a vintage 6-screw one.
The 2-point type usually pivots on two knife edges and those are the only points of contact with the guitar (when the trem's in use), whereas the 6-screw has 6 knife-edge contact points
and the bridge baseplate stays in contact and "rolls" on the body - so there's more friction but arguably better tone/sustain.
For my two new Strats I've gone for vintage(ish) trems - a Gotoh unit like the ones Suhr use and a Wilkinson/Gotoh VSVG. The VSVG has a neat design touch - still 6 screws, but 5 of the mounting holes are wider and oval-shaped so the bridge won't "stick" if all 6 screws aren't perfectly aligned.
Another thing I like about vintage-style bridges is that they're well suited to being blocked in place if you decide you'd rather have a hardtail after all (of course you can also block a modern trem, but it's not as neat somehow).
would the be any advantage to removing the 4 middle screws to make a 6 screw trem into a 2 screw one?
I don't think it's recommended to remove the middle 4 screws as there'd be too much strain on the remaining two screws and the soft wood supporting them may give way (which is why 2-point trems almost always sit on machine bolts screwed into threaded bushings).
But I have seen a trick where you set the bridge with all 6 screws then loosen the middle 4 half a turn, so they're still supporting the bridge, but not interfering with its performance so much.