All depends on your needs and desires, fixed flange gets my vote every time, cheapest, easier for add on's like bike racks, blade type stabilizers and so on, (also added bonus of built in parking sensor but I haven't said that, lol) But people who love their cars say that fixed flange are ugly.
Detachable, The most expensive, very nice, neat when you aren't towing as you can remove the ball when not towing but it all depends if you find towbars an eyesore or not, only certain types of bike rack can be used.
Swan kneck jobs are mid priced but less versatile regarding bike racks and things