This is a tough question! If you were to ask my sons, they would pick
Disney's Contemporary Resort every time while I would pick
Disney's Grand Floridian Resort & Spa each time. It really comes down to a preference in style and theming.
At the Disney's Contemporary Resort, it is always a treat to watch the monorail coming and going throughout the resort and to have the freedom of being able to walk to the Magic Kingdom. The rooms are large at 394 sq feet. The bathrooms, however, don't have a sink area outside of the bathroom, so there can be limited privacy. I do like that if you are in the resort during a heavy rain storm, you can easily move around the resort as it is housed within one building.
At Disney's Grand Floridian Resort & Spa, the resort is more "girly" (according to my sons) with its Victorian decor. The rooms are the largest at 440 sq. feet and have bathrooms with sinks outside the shower/toilet area. I like the bonus amenities of robes and nightly turn-down service at the resort. If you stay in the main building, you will be offered concierge service and be under one roof in case of rain. By staying in the main building, you are in the heart of the resort and all of its activity, which can be exciting but also noisy. If you'd like the concierge service but less noise, there is an outer building that offers that.
To help explore each of the resorts further, you may want to visit allears.net and do a search for each of the resorts. You'll be able to see another set of photos that will compliment those at the Walt Disney World website. Similarly, touringplans.com has detailed articles on both resorts and explores the pros/cons of each. As you continue planning your first trip, please let us know how can help. -Kara