We loved our Trastevere apartment during our weeklong Rome visit, but in Paris, have stayed in the Latin Quarter (Hotel Familia - numerous times) and at an apartment in the 2nd Arrondissement, a block away from Rue Montorgueil. For our apartment stay, being so close to the great fishmongers, the Stohrer patisserie shop, and other vendors made food shopping easy and fun, and we had superior ingredients! That was a bit like the neighborhood streets close to our Trastevere apartment. The Metro was pretty close, too, as were some fine restaurants, and we weren't far from the Seine, the Louvre, and the Pompidou Center.
The Hotel Familia in the Latin Quarter, a pleasant walk away from the Luxembourg Gardens and close to the Cluny Museum, the Monde Arabe Institute, and lots of budget Middle Eastern and other cheaper places for a good meal has been a key part of our shorter & more affordable Paris visits.
If you use Rick Steves as a yardstick, he lists Trastevere as a good option in Rome, while he's always recommended Rue Cler in Paris as his "back door" neighborhood, although you might be surrounded by many of his other readers there.