American. Those are 2 major American hubs. Should something happen to cause a flight cancellation, you'll have more options for rebooking.
Also, always, always choose the direct flight when possible!

AA for that - a phoenix to Charlotte flight is pretty much definitely going to fly because they needs those planes routed between those two hubs. Frontier can get cancelled and there's no backup.

American. Frontier is the worst (well the second worst, with Spirit being the worst).

You can always check their stats on on time departures. Non-stops are always preferable for avoiding delays. American is likely to be more comfortable than Frontier but not more than average.

I have to take an overnight flight from PHX to CLT in Sept. I try to avoid red eye flights, but I have to be in Charlotte early the next morning. My two options are 1) American Airlines flight, nonstop, 2) Frontier flight with a stop in Denver.

Which airline is most likely to get me where I am going on time? (most important)? Which one is more "spacious" for sleeping?

Thanks! I have never flown either one.