Most of DK's attacks may be faster, but that most certainly does not mean that Mewtwo has no way of being quick as well. One could probably bet that both Mewtwo's neutral air and his forward air are faster in activation time than anything DK has at all. The problem with these moves is their range. The range problem is easily dealt with though. You simply have to move faster than your opponent and be on top of them before they can react, and that is a question of skill, not really character.
Mewtwo's up air and back air have very nice range. The problem is many Mewtwo players don't take full advantage of the range and get too close when performing the attacks. I would say that proper bair play can be at least equal with anything DK would do in the air.
DK may have a better combination of quickness and range in the air, but I can assure you that it is not so much better that it will decide the match on its own, not by a long shot.
Mewtwo also has something DK does not have. A variable that can completely disrupt an opponent's combo or cause them to pause long enough for you to take advantage of it; projectiles. Proper use of the shadow ball can completely nullify the effects of an opponent's superior air game(and land game) to the point where it doesn't even matter anymore. Having a shadow ball fully charged up is a mind game in and of itself. The enemy will alter their approaches drastically, unless they desire to get smacked right off the map. With this altered approach, the enemy has a higher chance of making mistakes.
With the speed that is possible with Mewtwo, you also have the ability of avoiding everything DK does much easier than when fighting faster character. This is a very serious advantage that should not be underestimated. With no projectiles to worry about, it makes the dodging and out manuevering that much easier. If everytime the enemy attacks, he misses, then that is a serious problem, no?
For other miscellaneous information; forward tilt and down tilt both have impressive enough range and speed to deal with DK on the ground without trouble. DK might have greater aerial transversal, but as a character, overall, Mewtwo is definitely the faster of the two.
Yes, DK has some advantages, but he has nothing that will automatically make him win any match against Mewtwo.