I think you do the math and talk through the consequences with him. Graduating with no debt is a huge advantage to be able to give your kid. But to an 18-yr-old, that feels very amorphous and vague. Can you map out first what he can do with the extra $60K from the state school and then what the loan payments would be from the private option?
But also, what are the degree options at each place and effects on potential job or postgrad options? Does one school make it more likely than another that he'll be able to graduate in 4 years? (My nearby public is infamous for not having enough class offerings to get kids what they need to graduate on time -- and adding extra years in school can certainly increase the cost beyond what a 4-years-to-4-years comparison)
Also, which school is the best fit for your kid -- and how important is that? I have one kid who would be fine at a big public and one special snowflake who needed the extra handholding of a smaller school; for her, I forked over far more than I ever planned because she needed that support to fledge. (it paid off, btw -- one semester left, engineering major, A average, job offer in hand)
Finally, consider the difference in the athletic program. Is one more competitive than the other? If he'd be a big fish in a small pond at one and a bench-warmer at the other, it may be worth chasing the experience of actually getting to play. Also, if my kid were an athlete, I'd actually tend to veer away from the top-level schools (unless my kid had a legit shot of going pro), because the physical, mental, and time demands would make it very, very difficult to do well in classes and graduate on-time. Even at my DD's small school, a friend of hers who is both an engineering major and on the football team has now dropped a year behind, because once he got good enough to start, the demands of the sport were too much to stay on track with the academics.
Oh, and second the need for a major backup plan. He could get injured, he could decide he wants to drop the sport, he could get booted from the team -- all sorts of bad things can happen. What is the school's policy if, say, he gets injured in a game and can't play? Does the team honor the scholarship all 4 years, or is he on his own? What does he do then? Kids his age tend not to want to think about those things, because bad things only happen to other people. But going through the analysis is a very important lesson -- you always, always need to cover your downside risk, no matter what that is.
IMO, the state school should be the default, unless there's a really good reason to justify the extra $$$. But you should still do the full analysis so that you and he know that he's ultimately making the best decision for his circumstances.