Hi James! I'm always searching for the least crowded and cheapest times to visit Walt Disney World too. While the summer is a popular time for Disney vacations, some weeks are less crowded than others. The later in August you can go, the less crowded the parks will be, since many children begin returning to school in mid-August. For this reason, I'd choose the August 13 - 20 week over the prior one; attendance levels in the park will be lower for the latter part of that week. (If you could visit during the last week of August, you'd face even less crowds.)
Disney often releases
Special Offers during periods of lower attendance and traditionally late August and early September travelers have gotten some great deals on Disney vacations. Thus, the later in August you visit Disney, the better chance you'll have of being able to take advantage of a discounted room rate or vacation package. Furthermore, value season (when the prices are lower) begins in early August at many of the resorts, and the value season rates at many of the deluxe resorts dip even a little lower later in August, so you'll likely find better resort rates at the end of August.
Wishing you a magical vacation! Come visit us again at the Moms Panel if you have more questions! We're happy to help!