Pitt Honors has a very loose structure, you can make of it what you want. The main advantage for my daughter has been priority registration for classes. She is super involved (not pre med, pursuing genetic counseling) and has had a TON of opportunities. Having UPMC right near campus is huge, she got an internship this summer and has a job in a lab. All of her pre-med friends have taken advantage of the med center. Lots of related activities too, pre health fraternity, etc. Being in Honors College has nothing to do with getting jobs and internships.
Penn State honors is MUCH more selective. I can’t speak to what you gain from that but they don’t have a world class medical center near campus if I am correct.