Heh... where to start... everything alters the way it "drives" and sounds! Different music has different demands, and although it is definitely possible to do anything with any bow given enough training and skill... well, the right tools for the right job always makes things a lot easier!

On the physical construction side: different wood types, cambers in the bending, width of hair, type of hair, different styles of construction (fluting or not), different methods of fastening the hair (screw or clip)...

On the "finished" side: different weights, different balance points, different distribution of weights through the bow length, the exact method and application of carving and bending....

That's just off the top of my head! Each bow is quite individual in sound and response, even if they are the same maker and otherwise very similar with every other quantifiable measure... little things aren't exactly the same (down to the wood graining) and that alters things enough for someone to notice in the hand!