Hi Laurie:
While any time is a great time to visit Walt Disney World, after confirming with northern mom
Erin and northern transplant mom
Suzannah, if I had to choose between the two proposed times, I would lean towards April.
Both Thanksgiving and April break tend to be crowded because so many schools are not in session. However if you plan to stay 9 days, you'll likely notice that Thanksgiving will not be as crowded until Wednesday, giving your party more elbow room for a few extra days. Because schools around the country tend to have rolling-spring breaks, the Parks are generally crowded mid-March through April. (advantage Thanksgiving).
While you'll likely be able to swim most days during thanksgiving, the weather will be much warmer, may be even the high 80's, during April. So if you plan to spend some time at the pool or at a water park, then April may be more comfortable. (advantage April).
Also, it stays lighter later during April, so if you love late nights, the extra hours of daylight may make a difference to you. (advantage April).
Either way, make sure you plan as soon as you can and make Advance Dining Reservations since the Parks will likely be somewhat crowded during your stay.