This is a tough one! Even if loading the 'Ajax' URLs (is it JSON formatted?) is slow, with some smart caching this doesn't have to be that big of a problem. But since the metadata in the HTML pages is richer, I would prefer that. Website markup and Ajax URL parameters or JSON content will change all the time (breaking the channel), but with some smart xpath queries you can usually survive small changes.
This particular situation, the Ajax is not JSON. It is one of those basic html pages that comes up when you look at the network that you would use to get past a carousels on a page.
So how would you adjust the caching? Would it be the adjusted for the whole channel or just the individual html or json pull? And what value would you give it like a daily cache?