There's a few benefits to resilience over stamina.
The first one is limiting the luck factor. Crits are what kills people in arenas. If you get crit by two or three people at once, chances are you're dead. Reducing the chances of that is well.. a pretty big deal.
Without any resilience, if all 3 people hitting you have a 30% chance to crit, there's a 2.7% chance that you get crit by all 3 at once.
With 200 resilience, that goes down to a 1.56% chance, and it reduces the overall damage you take from those crits by 10%. So if you get burst for 7000 in crit damage in that time, that's equivalent to an extra 700 life that doesn't have to be healed (mentioned more in the second factor).
Now, the other benefit of resilience over stam is that it reduces damage taken. Stamina is just a buffer and you will need to get healed eventually. In arenas, especially with MS on whoever's being attacked, the healers on your team are capable of pretty limited hps heals. The less damage you take, the longer a healer can keep you up, and taking less crits while having the ones you take do less damage do exactly that.
In 5v5s, we've ran in and literally killed someone in under 3s of attacking them. Its not the most common occurance, but it does happen. I can almost guarantee 80% of the damage done there is crits. Negating one of those crits and having the rest do significantly less will usually mean surviving long enough to get some heals. We've also had occurances where our assisted target is getting tons of heals (usually when something's gone wrong) and we just can't beat him to the ground without a lucky string of crits.
Basically, the whole point of this is that crits are an *extremely* important part of being able to kill someone in arenas, and being able to avoid then will increase ur survivability by a lot. Stamina can only go so far, especially if you're taking more damage than your healers can heal, its only a matter of time.
A third thing that just came to mind is that crits also proc a lot of debuffs. Deep wounds and ignite come to mind right away, but I'm sure there are others as
Edit: Levk, I agree that you probably don't need resilience on your whole team, but it's not a bad stat on the people that are most likely to get focused. That and it comes as a standard stat on most of the best stamina gear in the game anyawy (GM / Gladiator).