Both of these schools are attractive to kids seeking different kinds of experiences, and kids I know who have attended these schools have liked them. I don’t know kids who considered both, probably for that reason.
Denison, typical of more isolated LACs, will have most entertainment and activity on campus whereas Case gives kids easy access to entertainment and activities that are independent of the school by virtue of its urban location. As a result, Denison has more of its energy stay on campus and in its community whereas it gets dissipated at schools like Case where students can leave campus for dinner, music, etc. All the students I have known at Case (a small sample size!) joined frats, (including ones that seemed unlikely to do so), so I am guessing that this is one way students create that community and keep energy on campus.
As an athlete, the team is likely to be the strongest social circle – because of time involved, sometimes being out of sync with the rest of campus, travel, training trips, etc. It’s easy to see how they can influence the choice. As a parent of a kid whose suffered a sport-ending injury, I wouldn’t recommend choosing based on the team if he likes both (even if he feels more connected to one.) I’d base it on the kind of college experience he prefers.
I’d also suggest looking at course requirements for all students as well as for his planned major and then mapping out 4 years using the course catalog. Sometimes, some pretty big (and meaningful) differences may appear. This may also have an impact in terms of study abroad (if desired) and how coursework intersects with the sports season.
I don’t think you can go wrong with either. Personally, I like LACs because of the commitment to community and the experience that creates, and Denison is getting SO much right. But that doesn’t make it the right choice for everyone.