Both good times. Here's some things to consider.
1. If staying on site, rates go up a bit starting September 30, so if you check in before that, you'll get a slightly lower rate. If you keep reading this board, you could find out as soon as there might be some discounts available.
2. We've been there the last week in September 3 times and crowds have been low. It's still hot and humid (to me) and brief afternoon showers are common. But not as hot as summer. The weather probably wouldn't be much different a week later.
3. Food and Wine Festival at Epcot starts 10/1 this year, I believe. The first week end is usually busy. We went for the first time last November and had a great time sampling all the different foods. It's a fun time to be at Epcot. We wandered around the World Showcase, splitting food and did that for lunch or dinner 3 times.
So, there's some pros and cons for each week. Hope you have a great trip!