If you are going to run separate subwoofers, a crossover and an amp for the subs are the way to go.
This is called bi-amping, using a separate amp to power each of two frequency bands, high and low.
Running a full-range signal into both the tops and subs would make for a lot of problems in the range where the boxes frequency response overlaps. So, in comes the crossover.
Some full-range boxes, like your average 15" with a horn small PA box, can be bi-amped as well, but mostly it isn't worth the effort.