[1] See a review about it that explains his findings. https://www.theatlantic.com/magazine/archive/2016/05/how-ani...
I am not really aware of any mammal behaviour that I cannot somewhat relate to at gut level. You may say I anthropomorphize, or you may say I equate, it doesn't really matter. There isn't a physiological or neurologic feature we don't share, me and all those other mammals. I have some language and some reasoning power to top it all off with, but our sensations, reactions, emotionals, motivators, fears, pains and joys are clearly of very similar nature. Of course they are - they run on the same basic hardware architecture.
And now, if you will excuse me, my dog wants to go for a walk. I know exactly what he means.
[Edit: typo]
If you want to find where our perceptions differ from that of a cat or a dog or an elephant, I believe that anything cultural or learned in nature is a better place to start. If every human experiences it, it's likely that other mammals experience it too on some level.
I suspect that if our experiences shared few or no similarities, humans would've had far less success in the way of keeping, training, and befriending animals. The ability to accurately empathize with other creatures has to have jump-started the process in many cases.