I will be at a resort half way between the two. Have a choice of flying into either.
Plan is to spend a couple days wherever we fly into.
Any benefits for either city? One more interesting than the other? We would not have a car, so is one easier to explore than the other?

Spent an evening in Bari decade and a half ago (coming in from Dubrovnik by ferry before heading onward the next morning). The (rather compact) old town by the port is the attraction (not that we got there) but the "new" town seemed rather nice and lively. Found a pizzeria serving assortments of delicious hot/warm antipastos which seem to be a rarity. Brindisi (flew out of there after the end of a cruise ~50 years ago) seems to be more of a port city than Bari (which is also a port city) but was also the terminus of the Via Appia.

Bari airport is a bit further out of town than Brindisi (we bussed to pick up the rental car at the former) while the latter is pretty much right in town.

You could get a car to explore Matera (the old town is excavated from tufa) and Alberobello (trullis) and stay out there. If you are arriving early enough in the day, I'd just rent a car (driving there isn't that bad) and stay in either of those two places.

I'd pick Bari if only to have spaghetti all'assassina (an unusual pasta that originated in Bari).

I spent 3 days in Brindisi 37 years ago (I had to do a major repair to my car)! The only "exciting" thing was to watch the cigarette smugglers preparing their boats, i.e., loading bottles of water, etc., but I never saw them coming back (during the night). I doubt, though, that the spectacle is still available; therefore, the only thing that is a "must see" is the scalinata at the very end of the Via Appia, at the waterfront. On the other hand, it is much closer to Lecce (not far from the tip of the heel of Italy), which is a very, very beautiful city, clearly worth a visit!

Bari is a beautiful city but probably worth a night or two max. The fish market is a cool experience. Brindisi is way smaller - a day is enough. Quite a few foreigners for a city of its size because the airport is one of the logistical hubs for the UN World Food Programme.

If I may, I�d reconsider not renting a car - Puglia is one of the most scenic regions in Europe but public transport is bad. With a car you can really see some gorgeous places (such as Lecce).

It is going to just be a couple days to get our feet under us. So we don’t need lots to entertain us. Lecce sounds interesting. I really hadn’t thought about renting a car, but since I have to end up back at the airport to catch the ride to the resort, that might make sense.
Originally I was just thinking can ride from airport to one of the cities. No reason not to look a bit further afield.

A follow up question, since it seems there are some folks very familiar with the area.

We have a choice of dinners and time out in one of the following towns. All have great restaurant choices that is provided, so the food isn't primary driver.
Which would be the most interesting to spend an evening. Leaning toward Poligano a Mare, just based on google pictures. But open to any.

Ostuni

Polignano a Mare

Monopoli

Monopoli is great and is the place I chose for several days as a base (AirBnB) alongside Lecce (Hilton) on my last visit to Puglia. But if it's just for an evening I would go with Polignano.

vote for Polignani a mare

Puglia in 2024: we did Lecce, la Grotta Della Poesia, Otranto, Galipolli, Ostuni, Bari, Alberobello, Locorotondo and Polignano a Mare.

All places were fantastic and indeed, Polignano a Mare is on top of the list. We skipped Brindisi. So many good places to eat in Bari