I don't see why people are comparing Providence to Hartford. It should be more properly compared to New Haven.
Providence v. New Haven
1. Brown, Prov. Coll., RISD, Johnson & Wales = Yale, UNH, So. Ct. St. U., Albertus Magnus Other than Yale, Prov. is much more "connected" to its colleges. Plus, Yale didn't give a about the surrounding neighborhoods until about 10 years ago. The improvement since then has been astounding.
2. Great ethnic food in both places / I think fine cuisine is so-so, not great, in both cities (Prov. has a great French restaurant near the banks below the East side, NH has the Union League cafe. New Haven has a clear edge, IMO, in both "ethnic" food and fine dining. Nothing in Providence can touch ULC, Zinc, Caseus etc . . . . What NH needs is a take out lunch place like East Side Pockets on Thayer St. I almost never miss a chance for a Gyro pocket with the works . . .
3. Pretty good bar scenes. Getting a bit old for this, but my experience is that they are roughly equal.
4. I'd give an edge to New Haven's theater and arts scene. New Haven's galleries and libraries associated with Yale are world class, while Brown doesn't have anything like that. Yale Rep. Theatre and Long Wharf are well known. Clear edge to New Haven. Hartford Stage is better than Trinity Rep as well.
5. Access to big cities: NH is 1 hr. from NY by train, Prov. is 45 mins. from Boston
6. Access to pretty good beaches: Prov. is about 45 minutes from Little Compton and Horseneck, New Haven about 35 minutes from Hammonasset. Clear edge to Prov., though the better beaches are to the west, particularly Charlestown, East, and Weekapaug. Horseneck is a hole, though cheap parking is a positive. You can't go in the water after the end of June due to massive drifts of red seaweed.
7. The only thing Prov. has better than New Haven is better hotels and a better downtown mall, if you're into that sort of thing.
New Haven doesn't have the high end shopping that Providence has put in PP. Some of the chains have streetfront stores near Yale.