From a logical standpoint, being a quadruped surely does increases the alien's speed when running. But when it comes to crawling on walls, overall movement speed etc, I'm not that sure.
Quadrupedal animals are, most of the time, faster than bipedal animals when running. Although you have to take the size of the animal, the size of the limbs, the overall body structure etc... into account, I think its safe to say that, when running, the Dragon is faster than a "normal" alien.
The only thing that could really alter the Dragon' speed when running are his legs. They're not really conventional quadrupedal legs. Being very long and more of a hybrid between bipedal and quadrupedal. And the way the alien was running did look rather awkward because of that.
"Normal" aliens have these long and strong legs, I'm pretty sure that they could run at great speed if needed.
When it comes to running, I think that the Dragon is faster. But when it comes to reflex, overall movement speed, crawling etc... I don't think that there's a big difference.