I guess it's *capable* of doing all the stuff you mention.
But yeah, you'll need to script for it.
Only cross -browser tests I have run on Chrome & IE and, as you say, it simply runs the same set of tests twice. Once on Chrome, once on IE. I get sets of results back for each. I don't specifically highlight differences between the two But I could easily extend my framework to do so if need be. For our use, IE is a "nice to have" seconday consideration. We don't always run that part. Chrome is the key part.
The other issue I ran into with this is while the object model is almost always the same (I did run into a site built with Ruby where the DOM showed differences in TC's object browser - but it was work-round-able), some of the other elements of browsers/pages are not. How style information is reported differs between IE & Chrome. How you start the browser with a certain page is different. How you tell if page elements have fully loaded is different.
So yeah, the bulk of things worked. But I did have to code in some branching to account for areas where it didn't.
Mind you, browsers and sites are a lot more complex these days. Anything that is truly going to be 100% cross browser compatible, out of the box, would have to be very clever, and very complex! And would likely require frequent maintenace patches to keep it in line ....