If you plan on relying on bus transportation to the parks, the Doubletree Service isn't as good as the Coronado will be. I've never stayed at the Doubletree, but I have stayed at the Grosvenor. The buses don't seem to run as frequently, and they leave you off in the middle of a parking lot as opposed to an actual spot. I've never been comfortable waiting in the parking lot for the bus, especially with kids in tow. That's just me.
That being said, I'm not a big fan of the Coronado Springs resort. I don't like the set up of their food court (nor th fact that they charge a 10% gratuity or service fee or whatever they are calling it to your meals when you eat there). I found the resort to be very noisy, and the walls paper thin. We heard the footsteps of the people in the room above us, and voices and TV of the people in the rooms around us.
Like everyone has said, it is definitely a personal choice. I know that I prefer to stay right in a Disney hotel for all of the conviences, and the fun themeing at most of the resorts.
Karen