You guys do know what destroyer's Critical damage are like, right? they deal about 3 times the normal attack. So in my opinion, going full DEX is better than STR, since Destroyer has high P.attack skills & passives, so it would be better to have critical to triple the damage.
Anyways, about the critical Sword VS Axe....
I guess you already know that the skill " Rage Burst ", which increases Critical damage by 15%>18%>20%>21%>23%>24% It only works with Swords...
Source :
http://forum.celestialuna.com/index.php?/topic/2491-rage-burst-facts/
While Axe could only get axe mortality which increases 12,5% critical damage for the max level. So I think sword would be a better choice for greater damage