I was at Penn last semester from Edinburgh. *most* exchange students at Penn from the UK (UCL, Edinburgh, Imperial, Kings) were disappointed by the academic standard at Penn. This is more due to the US style of education than Penn as a university. More focus on being taught, group work, and continuous assessment which isn't necessarily a bad thing. You can't really say the UK or Edinburgh is less 'rigorous' though - the biggest difference between Penn and Edinburgh for me was that no matter what, I have to know pretty much all of a course for the final exam at Edinburgh. Most courses follow the same grading procedure and structure. At Penn, no real final exams makes not understanding certain sections of the course okay. In 3 of my Penn courses most of the course material was not tested explicitly. Courses and marking are very variable though.
In terms of comparing reputation just remember there is a huge difference between private and public universities in the US. In the UK and other commonwealth countries universities are generally seen as public institutions. This influences the differences in teaching, reputation and expectations also. Many people even at Penn admitted to going there simply because it was a private Ivy. People don't really consider universities in other parts of the world this way, Russell League is a much weaker brand.
Edinburgh stands up well for a public institution, and you really have to look at specific fields if you want a good idea of reputation. Penn, for business, is world renowned. Everything at Penn is connected to Wharton. Edinburgh, for Informatics, English, Geology, etc, is well known. During my time at Penn and at other universities, people in these fields would often bring up the fact that they/someone they knew had done something at Edinburgh in one of these areas. Some people would literally rant about it. This is good. Outside of these areas it would really never happen. The same for Stanford vs Ivy league in say Computer Science - Stanford blows them away. It's really hard to make these comparisons and a mistake to look at newspaper rankings and try match places across countries. Why do Oxbridge only equate to Ivy League and Stanford not fall up there? Even CMU is much better for CS than Penn.
Overall I was really disappointed by my academic experience at Penn. When I went I really thought in the way that Ivy League = Oxbridge and I was going to a better university than Edinburgh for undergraduate education, in a way you describe kthomash. I was very wrong. I got more attention and answers in lectures, but when I came back to Edinburgh I got most lecturers to set up Piazza for their courses and our classes benefit a lot. It's not like they're unwilling in the UK, they're just stuck in old ways. Penn was a really 'nice' place though - University City is a much better place to be a student than Edinburgh. I'd say there's no equivalent to Edinburgh in the world, which holds true for every other university. They are complicated things and the only fair comparisons are not even just in departments but specific specialties in departments (eg Computer Graphics at Penn vs Natural Language Processing at Edinburgh). Reputation within specific fields is a huge thing. Talk to academics, you will be surprised. Informatics in general at Edinburgh is ridiculously more difficult than CIS at Penn. I was actually quite bored at Penn.