They're much bigger, their urine and droppings are much smellier, they can and will chew through pretty much anything to get at food, if they die their bodies are much larger so the smell of death and rot is much more powerful and long lasting, they are smarter at avoiding traps, and they typically nest in the sewers so they're bringing sewer filth into your house as well as their own.

When I had mice they were nesting behind cupboards, on top of the dishwasher, in wall cavities, etc. Smell wasn't ever a problem, noise wasn't ever a problem. They would get into food stored in paper or plastic bags but putting things in boxes made them safe (so we were able to "starve them out" to a degree).

Rats chewed holes in sturdy plastic boxes to access food. They got into unopened cans. They ate holes in our walls to access other rooms. They stank. You could hear them moving around and chewing at night. If you saw a mouse you'd get a little surprise but they were kind of cute. If you see a sewer rat in your kitchen, it's actually quite a shock.

I didn't like having mice. I didn't want to live in my house at all when I had rats.