It depends on what tier you talk about.
By portrayal, dogs in general are given more screentime and attention. And it's true that dogs would win due to better AP and defensive abilities (even if they lack mobility). However, does that mean cats stand no chance? I think not.
Look at these feats:
Their mobility is insane, and so is their CoO. They're capable of avoiding and pressuring dogs into battle of attrition.
But even other than that, their AP is no joke:
With that said, I'd say dogs would still win at about high diff, but cats can have a chance at outlasting them through hit and run tactics.
But that's low and mid tier.
If we move towards high and top tier, cats low diff:
And it's not even close.