I used AT&T Next for a past upgrade but all subsequent upgrades have been via Apple’s program.
If I recall, the prices were similar. The biggest thing for me was that phones sold directly by Apple - even if an AT&T phone - are not carrier locked from the outset whereas phones sold by AT&T are locked to AT&T.
Once an AT&T locked phone reaches 18-24 months (time may vary by plan), the subscriber can request the phone be unlocked. My experience has been that AT&T has been good about that when I have requested unlocks for old work phones. The annoyance is that the phone needs to be factory reset in order to get the benefits of being unlocked.
With the new phones supporting dual SIM (1x physical + 1x eSIM), having both locked to AT&T for the upgrade period would be useless for when I travel overseas so having an unlocked phone from Apple is my preference. Plus, for those with an Apple Card, there is the cash back on the monthly payment which would be higher for the Apple IUP vs AT&T Next.