A better university matters only if you're able to take advantage of what it offers. While the core curriculum is more or less the same for all accredited colleges / universities, a better university gives you access to a larger selection of advanced courses, proportionately more well known instructors, and better labs and facilities. However, the pace of a better university is higher, the hours are much longer, and the competition from fellow students much stiffer than in high school; the transition can be very jarring. Only you know whether you're talented enough and able to put in the hours (the latter can substitute for the former to an extent) to do well enough as an undergrad to make it into a post-graduate program, but understand that the bar is generally pretty high.