Well, as I stated before I am in the industry. I love adventurous food and outstanding service. We would also like to dine in a restaurant with a waiter that can speak english.
Some of our best meals were at Daniel in NYC, Gordon Ramsey's in London, and Kikunoi in Kyoto. All very different. Daniel was slightly "cutting edge" at the time, Ramsey was cooked to perfection, and Kikunoi was a perfectly delicate, seasonal experience.
I'm sure that we will have a good experience at anyone of these restaurants, but with this being our first trip to Paris, we would like to experience the best and have as much fun as possible.
Top services in town are definitely Savoy, le Cinq, and le Meurice. Le Meurice has an awesome pastry chef. For cutting edge, Gagnaire and l'Astrance are your best shots, though you won't have molecular stuff anyway. And there's l'Arpège, with a very warm service, a minimalistic approach to cooking that often produces some wonders, and prices that are impressive.
Have eaten at all of the Paris 3* with the exception of L'Astrance.
Our favourite is by far L'Ambroisie.
We have been lucky as some say the service is formal.
We found that after the first smile, and question of the staff they were responsive, and the service is exceptional.
We have been there three times now, once for dinner and twice for lunch.
I have always felt that my money was well spent.
We found the ambiance at Rostang (2*) to be exceptional as well.
We are seniors, but there was a couple, who made us look like youngsters, and the Rostang staff, literally discussed at great length, each individual item on the menu with them.
They were not only patient, but were kind.
I was most impressed.
Dinner at L'Arpege, was well.. I have posted,... great disappointment.. and the staff were friendly, almost bubbly.
There must have been many "friends", as Sophie put it even in the evening, because there was a lot of hugging and kissing.
Our worst 3* meal anywhere.
Well, it's a question that comes regularly but we haven't seen it in a long time. Here's an old response (http://www.julotlespinceaux.com/2007/06/sil-nen-reste-quun-paris.html) that lacks recent updates (l'Ambroisie still extraordinary but not as great as it once was, le Cinq now has Briffard, Ledoyen is pretty good).
The best in town are Gagnaire, l'Ambroisie, l'Arpège, Ledoyen and le Cinq. At that point, I feel that Le Cinq just is the best because Briffard is not tired, he really is on fire, and he is an exceptional chef. Also it offers palace service and an incredible wine list. Gagnaire is a roller coaster and a gamble, always an interesting experience, not always a great one. But many had their best meal ever at Gagnaire. Passard (l'Arpège) is also a great minimalist genius, but he does not always deliver. Indeed Savoy is a unique experience for service, with excellent food. The most innovative ones are Gagnaire and l'Astrance. Ducasse is only on par with the others when it comes to price.
Another detail: best value among best restaurants is at le Cinq, Savoy (lunch menu only), Ledoyen. None of them cheap, mind you.
But to be fair, there can't be a objective hierarchy between those restaurants -- they are just different. The real question is which one is likely to be your favourite. Maybe you could give us a hint by telling us more about what your favourite meals were. Or what food you like.
I believe that a meal of this price deserves thorough preparation and personal selection, and I would strongly recommend reading excellent blogs like mine (www.julotlespinceaux.com and pics of more restaurants at picasaweb.google.fr/zejulot), Chuck's (www.chuckeats.com), Lizziee's (http://lizziee.wordpress.com/), Vedat's (www.gastromondiale.com) to make up your own mind. Many of them will be happy to respond your questions personally.
I have no experience with ADPA and only one with Gagnaire.
That said, I think I can say that you're looking at two very different restaurants here. ADPA would probably be the safest bet, and possibly a wonderful experience. Some will probably tell you it lacks some soul and emotion.
Gagnaire, I've been to. What people say is true: expect the best and the worst from your meal. At least if you go with the menu. The "à la carte" dishes seem more consistent. Nevertheless, it's really a great experience, and if you're feeling a bit adventurous, a truly great choice.
Why don't you consider other 3-star restaurants? It's not like there's no other choice in Paris! Maybe you should tell the board what you like/expect: you'll get very good advice, for sure.
Agree 100 percent with olivierb. You couldn't pick two different three star restaurants from Pierre Gagnaire and ADPA. I loved my threee meals at ADPA, although I do realize as a regular customer of Ducasse my experiences might not be that of a first time visitor to his restaurant. Also consider Le Cinq and if you want to experience the best in Paris consider Arpege.