But I should add that my area of focus was signal processing and wireless communications. In those fields, most of the "hands on" experience was actually coding and simulating various algorithms (same as what I do all the time working in that field).
So not quite the same thing as taking a small engine apart to see how it works. But that curiosity and interest in knowing how things work is a big part of what I was talking about above (and I did take things apart when I was a kid to see how they worked 🙂 --there just isn't a much opportunity to really do that with algorithms and electronics).
As far a the U and USU engineering programs go, I have a lot of respect for both (particularly USU, which is excellent in several engineering disciplines). I'm not familiar enough with either school to know what the hands on curriculum is like, so I'll take your word for it. But I don't think there is really a wrong choice among those three universities when it comes to engineering.