@blevine My daughter was in a similar situation - wanted to continue her sport at the D3 level. She could have gone to more well-known D1 schools, but preferred the smaller size of the D3 schools so went in that direction. It’s a very personal decision that has more to do with fit than prestige.
There is certainly a balance between hands-on and theoretical. In my opinion, you need a little of both to succeed over the long haul though there is a range of what works. You absolutely need the theoretical basis to progress up a technical ladder within a company. Some say you can pick up the hands-on aspect in your first job; but, that really depends on who you work for, how the work and training is structured for new hires, and what the expectation is. I have seen newly minted engineers who probably had a good handle on the theory, but couldn’t actually do the real work of engineering. It can be difficult to turn that around.
The knock against WPI is that it isn’t as theoretical as other engineering schools. The origin of that could be that so much time is spent on the two mandatory projects. However, most schools have a senior capstone project, I don’t see this as being any different. What is important is the quality of the project. Some are better than others. The additional project (besides the senior project) is the junior year interdisciplinary project, which is often done abroad, as mentioned by @HPuck35. You would have to balance the skills one would gain from such an experience with whatever the cost would be, whether it be one less class, less undergraduate research experience, etc.
I think the education at RPI is also hands-on, though some say it is less so than WPI. I don’t know if that is really true across all departments.
I have worked with some terrific WPI engineers, each of whom had a very good theoretical foundation and could hit the ground running. They have been strong contributors throughout their engineering careers. Both WPI and RPI students get into excellent grad schools and/or are well-employed after undergrad. RPI is definitely better known outside of the Northeast.
I second the suggestion to really look closely at what is offered at a Union College or Lafayette. I understand it is attractive to some to attend an engineering school in a Liberal Arts environment. However, any accredited engineering program will require a certain amount of math, physics, chem, etc. Engineering is very structured. So, there isn’t that much flexibility to take many outside courses,although the quality of the liberal arts courses at a Union would probably be stronger than at RPI/WPI. The Mech E department at Union is good, but small. This means there are probably fewer upper level courses offered on a regular basis. You would need to compare the undergraduate catalog at the various schools you are considering to see what is available at the upper levels.