Upon looking at their respective pages (and from actual experience playing the games) it would seem that both monsters have a similar enough speed that it won’t necessarily be a defining factor in the matches outcome. While Tigrex is certainly a physical powerhouse, as shown in this Mh4u intro video where he effortlessly knocks over large stone pillars during his charge:
I think I’ll have to go with Brachydios as the winner. The blue carapace covering his body is strong enough to resist the force of his own explosions, which is no simple feat considering that the slime coating his forelimbs and head is powerful enough to down an Agnaktor in a few punches as seen in this Mh3u video:
It also does help that Tigrex possesses a 2 star weakness to blast, meanwhile he has no elemental attacks that can give him an advantage over Brachy. So overall, I think Brachydios takes this 7/10.