Well, it was a long time ago, but I graduated from both of those schools. Did one of my undergrad degrees at GT then a masters at UCF, so I can discuss how they compared back then, at least. I'm a EE, not an ME, but I think the comparison holds for any engineering major.
The core concepts were comparable (physics is physics and one electron looks pretty much like another electron, after all), but the level of instruction was worlds apart. Too many of my UCF profs were recent PhDs who had no industry experience, but most of my GT profs were more experienced, had spent time in industry, and still consulted. (Example - I took all my E-Mag classes in the evening because a couple of guys from Bell Labs taught them after getting off work from the lab, and they were bloody good.)
Also, the student competition was much much stiffer at GT, with top students coming from all over world. Exams and grading were brutally hard to force a class curve, so to get A's you had to be among the very best competing against some very smart students. UCF was more of a commuter school at the time and didn't draw as many top-notch students. If you managed to squeeze a GPA of 3.5 out of GT, you probably could have gotten a 4.0 at UCF. GT had a tighter quality filter on its grads than UCF did.
Finally, the quality of resources (labs, equipment, computers, etc.) was much better at GT.
It's been a lot of years, so possibly things are closer now, but I'm doubtful. I hired quite a few grads from both schools during my career and there was some really good talent from both, but I was more likely to find it among GT grads.