Chantilly or Fontainbleau?

I've been to both. In my opinion, you can't lose either way.

Some unique features (which you've undoubtedly already identified in your research):
Chantilly - Horse Museum, horse shows, art collection
Fontainebleau - Napoleonic history

Extra thought (that you didn't ask for!!!!)
You are going to get recommendations for Vaux-le-Vicomte as an alternative to either of the above. Other than being a bit more difficult to reach on public transport than the other two, I would agree with any who urges you to research it. My favorite of the three.

If you still find the original alternatives equally appealing - I, personally, would probably decide once on the ground based on the logistics of public transport (timing of trains primarily) and how I felt. Neither is particularly difficult to access by train, but there can be a walk involved if taxis aren't sitting at the stations. The walks are not strenuous for anyone in decent shape. Train tickets do not need to be purchased in advance.

I decided on Chantilly. I am planning to fly home from CDG after spending the last two nights of our trip in Chantilly. It looks like about a 30 minute drive from Chantilly to CDG. We aren't spending any time in Paris on this vacation.

Fontainebleau looks lovely - I don't think there is a wrong choice.

That depends on your level of historical interest. If you're into Napoleonic history, the Chateau de Fontainebleau markets itself on the history of the Emperor and his time there. You see that too as you check out some of the souvenir shops.

If you're into equestrian matters, Chantilly is the place and it is also a famous chateau connected to French military history as it was the chateau of the Grand Condé, the victor of the decisive Battle of Rocroi in 1643. That momentous event is depicted among the paintings in the Battle Gallery in the Chateau de Versailles.

Ideally, both places are well worth your time and visit. If it's going to be only one, then my vote is Fontainebleau, obviously.

As already said, you really can’t go wrong. If you are interested in French, mainly royal history than Fontainebleau is the p(a)lace to go. You can find there influences of different periods of French history from the Middle Ages to the 19th century. It’s more than just Napoleon.

If it is simply put just for the looks, nothing wrong with that I would consider Vaux-le-Vicomte. However it has an intriguing story and together with it’s architectural unity it forms a well balanced stunning package. Certainly worth to consider in case you never heard of it.

Nevertheless Chantilly is fantastic too, it was my first château in France I started to visit. Many followed later, but can remeber well blown away seeing it for the first time.

I have visited all the three several times and as soon stepping inside not care much which is the best. I enjoyed each one of them in their own right, they are all fantastic and will do enjoying them once going back again. But as far as I can understand your question I would go to Vaux-le-Vicomte. Otherwise select the one most convenient going to.