Since I work at one, I stay at hotels free (within my brand) so I can't say I have much experience with airbnb. I do feel they cater to very different markets though, I don't necessarily begrudge the existence of airbnb, even if they are kind of our competition.
OTAs on the other hand, can all get fucked.
My hotel is a high-end dog friendly hotel, we don't require any additional cost for a guest bringing a room. Unless they order room service for their dog or something (yes, we have it).
We do need some additional paperwork, but nothing that most dog owners wouldn't already have on hand I think.