I have done both trips several times so I'll give you my two cents (although maybe you already booked.. if so, sorry).
TAP planes are in better shape than the SATA planes generally. SATA economy is rough.

If you stop in PDL, there's not much to see, unfortunately. It's not the prettiest city in the Azores or even among them, so take that into note. Much of the beauty can be seen from the sky if you aren't going to stop and travel around for several days (which I do recommend doing, the Azores are gorgeous).

It's very difficult to get any sleep on the short flight from the east coast to PDL. As soon as you finally hit that snooze, the lights are back on. So if you like to try to sleep on those overnight flights so you can function day one in your destination, I would go all the way to Lisbon.

And the MOST important reason I would caution you away from picking the stop over for cost: the weather in the Azores can be really really rough, especially in the winter. Anyone who visits often (like myself and my husband, who is Azorean and grew up there) knows that you need to buffer in the possibility of your flight not a)being able to land due to weather or b)having a lengthy delay due to weather. The Azores airports are small and although PDL takes in the most traffic, I have only been to the islands once when we didn't experience some type of travel disruption due to weather. I have, at times, been waylaid for days.

Just my two cents! I actually signed up for this website which I often view but never comment on to tell you this so I hope I catch you in time.