While many schools have say mechanical engineering, they do differ in what specializations they offer, how many tech electives they have, how the non-tech electives are handled and how flexible their programs are. The non-tech parts of the schools are very different (and these can often make the male/female ratios more even or add a lot of liberal arts flavor to your education). Many of the schools have specialties, Carnegie is comp sci/electrical, Case biomedical, Texas schools petro, Minnesota/Delaware chem, etc
States have invested a lot of money and resources to have excellent engineering schools, actually most states have at least one excellent engineering program, some have several.
Other things to consider are AP credits, direct admit vs. GPA requirements to get into engineering and then location, culture (frat, partying, etc) and other typical college criteria.
Visit the various schools as well, as you can.
Class sizes can be a bit misleading, most schools will have large freshman classes for chem, calc, physics, etc. The big programs like mechanical and electrical can have a lot of students, say at Georgia Tech (2000), but other programs or smaller students could end up with only 20 graduates a year. There are ways to figure this out here on CC or through lots of google searches.
Costs also vary widely, with some schools giving good merit and financial aid, so use the net price calculators and check on merit aid %s and financial aid availability too to make your final list.
Unfortunately, attending another state’s flagship can be very costly, especially Berkeley and UMich, so your own home state is often the cheapest by 10s of thousands a year. Merit and financial aid can be sparse to rare to non-existent.