3 main advantages are horse power, thats 450 (still could do with a bit more, want the 600 HP model), turning circle, and less compaction of the ground, plus the tracks will let you go when conditions wouldn't let you in a tractor a little bit more.
although you can and do have, and i've demonstrated a few this year, get tractors of that sort of power, the turning circles are crap compared, and you end up having to lift up, back up and scrub out your tracks a hell of a lot more when your doing the headlands of fields which is time consuming, plus the tractors of that size are heavy and the wheels compact the ground much more than tracks, and one of the main things i'm trying to achieve is to uncompact the ground, ready for the next crop.
it has a steering wheel, which is hyper sensitive, kind of throws you when you get back into your car after driving it for 12 hours or so, and wonder for a moment why your car isn't turning....
also has a decelerator pedal rather than an accelerator, which was interesting to start with, lol.