I stayed 5 nights at the Rive Gauche and it was wonderful! The staff was super. I have not had the good fortune of staying at the CE however I stopped by the hotel and the location is super. The pizza is good next door to the Rive Gauche but I hope you tried the Le Pavillon Montsouris 20 rue Gazan within walking of the Rive Gauche (best restaurant in Paris that I ate at). I would stay again at the Rive Gauche it is very quite and easy access.
I guess I would say each to their own regarding C-E versus Rive Gauche. But I will always stay at the Rive Gauche, not only because of such easy transportation and having lived in the area in the 80s, but also because of the superior quality of the hotel.
No, it's not as central as some others (though it is easier to get to than most, esp from CDG). Since I do my research at La Bibliothèque Nationale it could not be better, but even if not Paris is a relatively small city compared to most. If you get a good map from the front desk, you're at most a 10-min walk to the Ile-de-la-Cité etc. I'll leave Right Bank hotels to others -- I'm a Latin QUarter, Left Bank traveler since I love the history of the city in past times.
The Rive Gauche, in my view, offers the best of everything -- fabulous rooms and beds, high speed internet, breakfasts, cable TV, and easy access to Place d'Italie with all its shops (less busy than other stores in the more 'fashionable' neighborhoods) and also incredible Vietnamese/French food.
I'm totally biased -- I lived in the area for about 3 years, and I'd take it any day over Trocadero (one stay, would probably not return, even though the room was very nice). I have not stayed at C-E or Vendôme because I am on a research budget. But I probably wouldn't even if I could. Rive Gauche does everything I want or need in Paris.
Have fun! ProfC