I think the difference is that under a tax, air travel can still expand without bound as people are willing to pay more for the air travel, but if you cap emissions, then air travel can't expand, regardless of whether people are willing to pay more than the cost of the environmental damage.

(And yes, folks, the environmental damage from any one use is bounded; it can't possibly cost more than the cost to undo that damage. If your model of the environmental damage implies it is infinity, it's just wrong, and it's driving bad policy.)