So it's Dragonite the original Dragon versus Haxorus the axe wielding Dragon. I'll start...
Which one would win:
Well Dragonite has more bulk and a very useful ability "Multiscale", so it gives Dragonite an opportunity to set up a Dragon Dance, or to just 1HKO Haxorus with an Outrage. Haxorus has fair defences, but they wouldn't generally be able to deal with an Outrage from Dragonite. On the other hand Haxorus's attack stat is sky high and with the right conditions it could 1HKO Dragonite. Dragonite though would be the overall victor in my opinion.
Which one is more useful:
Well they are both very useful for mostly offensive roles and both of their better abilities are also useful. I would say they are on the same level for usefulness.
Which one do you prefer overall:
Well I love Haxorus's design and ability in battle, however my most favoured Pokemon of all is Dragonite. I prefer Dragonite's overall appearance, ability, and it's the mascot of my battle style.