I would think the school you attended would matter more for the "high tech" engineering jobs, at least for your first job out of school.
In other fields, such as civil, you really just need to attend an ABET accredited school so you are on your path to a PE license. Civil doesn't have a whole lot of "cutting edge" stuff you need to know, as high-tech would, and an ABET accredited school assures you've studied the fundamentals of civil.
Also, while the PE exam is given in a number of engineering disciplines, most PE exam takers are in civil, mechanical or electrical ("traditional electrical", not high-tech), because those are the folks that need to seal drawings. In the latest PE exam administration, there were about 9K-10K civil test takers, but only 20 software engineer test takers.
You just need to know where you want to go when you get out of school. If it is going to cost a lot, I would never advise going to the big name school when you just need the ABET accredited school. If you're in a field that requires a PE license, once you have the PE license, no one cares where you went to school.
