Disclaimer: I go to UMich. I can give you an honest opinion of what life is like as a student here, but know next to nothing of WashU over what grandalf has already said.

I'll get out the obvious out of the way: Michigan is cheaper. It's the most expensive public school in the country, but it's public. WashU is private; more expensive. I assume you know this.

There's something to be said for Ann Arbor--it's a very unique town. For the most part, almost the entire population of the town can sit in the Big House (the football stadium), so during the semester the town has a great young vibe. There's plenty of students living in most areas of the town. It's a great place to make friends. However, you honestly have to consider the weather. I grew up in a desert, but am fine with the blistering cold. I'll say this though: the weather, at least from what I heard, _is_ as bad as I was told.

The housing system has gotten better in the 4 years I have been here. The dining halls are now pretty awesome, and if you are able to live on Central Campus (definitely live on Central--West Quad or South Quad), you'll love it. As a freshman, you'll probably hate living on North Campus, and will be ambivalent towards living on the Hill. I'd highly recommend against living off-campus for at least your freshman year unless money is an issue.

Can't deny the school spirit. We're not a terribly rowdy bunch, but we love our sports. The Wolverines are known for excellent football (let it go) and ice hockey teams, and a re-emerging basketball team in terms of big sports. Every sport imaginable gets played at the varsity level though. Intramural sports are hugely popular as well, if you're into that.

As for the academics, Michigan is a solid all-round school. It excels at engineering and certain liberal arts, and has some of the top graduate programs at the university. You didn't specify exactly what you want to study, but there's brilliant research going on in almost every field where that is done, and you can get a piece of the action fairly easily.

You have to work to stand out. Expect intro chem (for example) to be 5 or 6 sections in a 500-person lecture hall. Other popular classes are exactly the same. Class sizes obviously shrink the further you go, and you get some more focused time with GSI's/TA's (all big schools do this) in discussions, but to be recognized by the professors you need to go out of your way.

I really have absolutely no idea how other schools do this, but at Michigan you're really encouraged to take a tremendous variety of classes. I don't know if this is something that appeals to you. For example, you'll find many mechanical engineering students in the 300-level philosophy classes because mecheng students are required to take a sequence of humanities/social science classes up to the 300-level and philosophy happens to be popular. Engineers very regularly get a math minor because it is encouraged given how much math you are required to take anyway. Economics majors very often double-major because the major is small, and the rest of the requirements for the economics major can be put towards other majors.

I've also found, for the most part, that the advising staff here for the specific majors are spot-on. Again, based on volume of students, you might not get someone remembering you semester-over-semester, but you'll get good advice without being judged on choices.

I'll assume that, given that this is HN, you're looking at CS. Michigan's CS is not the engineering department's strong suit, but it's still a very good program as far as I know. I have several friends doing EECS (electrical engineering and computer science), and, despite the tremendous workload, are enjoying it.

Remember: it's probably not wise to make a decision of this magnitude based on the ramblings of someone on a forum on the Internet. Go to the course websites of each school and look at the syllabus for each program. Look at what it costs to live in each city, what you like/don't like about each city etc.

If you make it to Michigan, good luck! I'm sure you'll have a fantastic time. I graduate next week, otherwise I would have shown you around in the fall, but you should do fine.