If I remember correctly, RaikouLover has always stressed the following point: "Don't use Dragonite as an inferior Salamence, as it is simply not going to work". Following this point, I think Dragonite should only be used on teams which specifically need a bulky sweeper or an effective stall breaker. Of course, for this, I need to bring up the actual topic of this thread.
As pretty much everyone else has stated, Dragonite has options to a lot of support moves that Salamence doesn't. These include Heal Bell and Light Screen. From this information, we can easily assign Dragonite two roles that would be much more difficult (or impossible) for Salamence: Cleric and Bulky Dragon Dancer. The problem with the Cleric set is, Blissey usually pulls the job off better due to a decreased amount of weaknesses, so I think Dragonite is best used on an offensively oriented team that takes advantage of its typing and bulk. The Dragon Dancer would work in a similar way, except Light Screen allows it to survive even Ice Beam, and Dragonite would make a fantastic switch-in to Heatran.
After all of this, we have the MixNite set. From my own opinion, I don't really find the MixMence set inferior to Dragonite when it comes to wall-breaking. Sure, Superpower OHKOes Blissey, but you still need to predict when using it. If Blissey switches into Draco Meteor and sees the Life Orb, of course it's going to switch out. In Salamence's case, the same applies, as Brick Break 2HKOes regardless (hit it on the switch-in, and after SR damage, Blissey is left at around 30%), and at that stage, Blissey is pretty much crippled. The best advantage in Salamence's case is higher Speed, which I find much more useful than an OHKO on Blissey that doesn't even matter.
That is all.