I like cats more, but if I was looking at this objectively, I think it'd probably be canids who took over.
Whenever they've been introduced in a new wild area that didn't have them, wolves became the apex predators with barely any effort, and almost every ecosystem with coyotes in it as the top scavengers is more stables than those without; dogs have probably more racial variety within the boundaries of a single species than any other animal on Earth, and they understand our civilized world (to the degree of being able to survive in it even without humans in it) better than most other animals. And they're a species that has a incredibly deep level of inborn cooperation and group instinct, which means they're more likely to develop a complex society - and that's assuming intelligence developed again, which it might not. So, unless intelligence is an evolutionary inevitability and opposable thumbs are a prerequisite for it (in which case, some other ape will probably get back there first), I think dogs and wolves are gonna outcompete everything else.
Just my opinion, that's all. :)
Although it does brings me to mind something I read once about how we, humans, are basically the equivalent of the fairy folks of lore when looked from the point of view of wild animals... here, I found the link:
https://www.reddit.com/r/tumbl...s_are_the_urban_fae/
It's quite an interesting take on humanity, and with us bringing about climate change, it also matches the "their words is fated to be destroyed and fall into neverending winter" aspect of the fae narrative. I found it quite an amusing idea to mull over.