Summer is mega busy anyway but does either month have slightly better attendance?
I think they're the same. If you're going by car you can look into the dates for black saturdays to avoid the worst traffic jams.
I most often go in August and it really isn't too busy (even though its summer holidays) as long as you are pro-active, have a plan and are prepared to do some waiting in the afternoons particularly you'll be fine.
We always make sure we make the most of fast passes, queue for rides such as Crush's Coaster, Ratatouille and Dumbo first thing in the morning and then we are flexible about what we do next. We usually go for a week and then spend 2 hours or so in the afternoon just relaxing at our accommodation and missing the busiest time of day.
Early July is marginally quieter as the English schools are not yet on holiday .... But I do say marginally :)