Hi, Megha!
Debating between resorts is always hard since each resort has its own special touches, so it can be hard to compare. But having stayed at both of these amazing Deluxe Resorts, I have to say that I prefer
Disney's Contemporary Resort.
Since you have little ones, I think this will be a good choice for your family. The proximity of the Contemporary to the Magic Kingdom simply cannot be beat. You are just a quick 10-15 walk from your room to the front gates of the Magic Kingdom. This will be particularly helpful for mid-day breaks. You can pop back to your resort for naps, a change of clothes, and you can be back at the park in a jiffy.
To get to Epcot, you can hop on the monorail inside your resort, and with a quick monorail change at the TTC, you can zoom over to Epcot. The monorail is a fun attraction all by itself, your 4 year old will love it. Animal Kingdom and Hollywood Studios are accessible by bus from this resort.
The Contemporary is also home to Chef Mickey's, a super fun buffet where you can meet your favorite Disney pals and get pictures and autographs, a fun splash area for the kids to cool off, a sandy beach, and a beautiful view of Bay Lake. You can book a Tower Room with a theme park view for amazing views of Wishes fireworks at the Magic Kingdom, or view the fireworks from the 4th floor deck if your room does not have a view.
If you decide to go with Animal Kingdom Lodge, you will not be disappointed! It is beautiful, and a Savanah View Room will allow you to see animals roaming right outside your room's balcony. The downside of this resort for me is the location. You will experience longer bus rides to the parks, making mid-day breaks more difficult. If you stay here, just plan ahead!
Whichever you choose, I hope your vacation is magical!
Cathy