There is no merit aid at Bates. Only financial aid. If all the money has been allocated for this year, that would probably explain why you weren’t offered FA.
I would say that Denison is a great school, but is probably regarded as a tier down from Bates, at least in terms of academics. My child is a 2020 grad. She has done very well for herself since graduating and the name is highly regarded.
Bates is in a small city/large town, with a real airport (PWM) 40 minutes away on a major fwy. It is not remote. Students can major and minor in almost anything and there is no core curriculum. It is very flexible. The concentrations are broad. My D took nearly every class she wanted to.
Do you want easy access to outdoor activities? Bates will be better for that. I’d say that Denison probably has a slightly more sporty vibe than Bates. These threads might help you get a better understanding of what Bates is like.
Bates is, imo, the better school, but I’m not sure it’s worth $100k more. Your biggest consideration is financial. If grad school is on the cards for sure, go to Denison. If you will definitely stay in the Midwest, Denison, but there will plenty of midwesterners at Bates.