Assuming that Haxorus is level 100, it is highly unlikely that a Pokemon will out speed it in general use against the Elite Four and such. If Haxorus had 31 Speed IVs, then it's hit 293 Speed (322 with a boosting nature) which is a lot faster than most in game Pokemon. In the Battle Maison however, more competitive sets are used which means items such as the Choice Scarf may cause them to be faster than Haxorus.
In online play, anything with more than base 97 Speed with full Speed investment will out speed Haxorus. Haxorus is more of an attacking more than a fast one, so it will often move second against Choice Scarf users, fast Pokemon, etc.
Is for the item, it depends a lot on the moves you are using. Since the freedom of choosing moves usually comes before dealing lads of damage in game, a Life Orb is the best option; Choice items or a Lum Berry may be considered if Haxorus were to be used online. A Muscle Band may also be considered, but a Life Orb is superior.
