I've had the opportunity to attend both public and private universities. Here was my experience with both:
Public university - My time at the public university I attended was phenomenal. Some of that had to do with the fact that campus life was generally pretty fun, but the main reason was that I got involved in a campus ministry that helped my faith grow exponentially. The name of the ministry is Cru (formerly called Campus Crusade for Christ), and the ministry skills I developed and the fellowship I experienced (probably the closest friendships I will have in my life outside of my friendship with a possible future spouse) are things that I still benefit so much from. The friendships I had there ran so deep because we were united as believers trying to reach the campus as we lived, ate, studied, and had classes with non-Christians. I got to see fellows students' lives profoundly changed by the Lord, and it was pretty incredible to witness. Also, campus rules are more laid back, so you aren't necessarily limited as far as what type of clothing you wear or having a curfew or anything like that.
The flip side of that is that you will encounter lots of people who go out and party every weekend. You'll also encounter all different kids of belief systems, but I really believe that this prepares you for real life in a sense. You most likely (and hopefully) won't be spending your time around Christians exclusively, unlike Christian colleges/universities where it tends to be kind of a bubble. You also may deal with some professors who are hostile towards Christianity, which can put you in a bit of a precarious position at times, but it's ultimately a good thing to be challenged in that way I think.
My experience at the Christian university was difficult because I was only there for three semesters and it was tough to make friends, so I will say that that does taint my view a bit. The huge pluses of Christian universities are that you have the opportunity to take Bible and theology classes that wouldn't be offered at a public university. You also have the opportunity to go to chapel multiple times a week, and you'll most likely not have to deal with the party scene nearly as much.
The downside, I think, as I mentioned before is that it tends to be a bit of a bubble, and doesn't necessarily prepare you well for relational ministry and living your life as an ambassador of Christ to the people around you like going to a public university and being involved in a campus ministry does. Also, the rules tend to be more stringent. Chapel attendance is often required, there is a dress code to some extent (ex. the school I attended wouldn't allow shorts before 4:30pm) that is enforced mainly by the RA's and RD's, and there will be some type of curfew.
Hopefully that helps at least a little bit
