That is a good question, and the answer depends on a lot of different facts. We can actually see very far if what we are looking at is bright enough.
With just our eyes, on a clear night, we can see a star in the constellation Cynus the Swan. This star is believed to be about 1550 light years away, which is about 9,000,000,000,000,000 miles away (very far).
The quality of our vision does decrease though. You usually need to be closer to things to see fine detail, the little details need to be a lot bigger if they are further away.
I believe cats and dogs can actually see about the same distance, but I think their vision is different because of the size of their eyes and the shape of their pupils. Cats will also have better vision in the dark. Cats and dogs have worse vision than humans though.
It can be hard to create experiments that test distance vision in animals, and they aren’t very good at answering our questions when we ask, even if we ask politely!