Hi Anna,
Thank you so much for visiting the Disney Parks Moms Panel with your question. This is a great question! You have chosen two fantastic times of year to consider visiting Walt Disney World.
The weather in early May and mid-to-late September will be about the same. For both of these months, the average high temperature is between about 88 and 90 degrees Fahrenheit. Because you are looking at the beginning of May and the middle or end of September, I think that you will find the temperature at both times of year about the same - just a little cooler than those monthly averages. I like this temperature for a visit to Walt Disney World. It is warm enough to unquestionably wear shorts, and to get into the pool every day, but it is not as hot as at the height of summer! Since both of these times of year are not traditionally times that children have vacation from school, you should also find that both times are not peak travel crowd times at Walt Disney World.
I suggest looking at two festivals held at Walt Disney World. The
Epcot International Flower & Garden Festival is held in the springtime, and celebrates spring with experiences such as lovely topiaries, seminars, concerts, and so much more celebrating spring and all its beauty. In the fall, Epcot celebrates again, this time with the
Epcot International Food & Wine Festival, which features food and beverages from all over the globe, and a wide array of experiences celebrating food and wine. If one of these festivals is more appealing to you than the other, perhaps you can consider booking your vacation at that time.
Please do let us know if you have any further questions, Anna!