kayakmom,
While I can't speak from direct experience (I've never attended a larger state school, nor am I an Engineering major), I wouldn't hesitate to say that the research opportunities will be much more abundant at a smaller liberal arts school with an Engineering program than at a flagship state school.
Almost all of my Engineer friends have been involved in at least one faculty-headed research project. These students may be EXCEL Scholars (see:
Lafayette College - Excel Scholars), engaged in independent study or conducting advanced research (for course credit), or completing an honors thesis.
Our Engineering program in general emphasizes "real-world" experience, or what we sometimes call "experiential learning." Many upper-level Engineering courses are taught as seminars, where students design and implement team projects.
- Justin