I've been visiting WDW since 1992 and, as an offsite visitor, my strategy has always been to avoid EMH (or EE as they used to be called) days at all costs. That strategy has served me very well. I've read reports here of people who have visited at exactly the same time as me who have reported heavy crowds when I've experienced the opposite, and on the few occasions when I've been forced to be in a park on its EMH day, I've been proved right. Most recently we visited Epcot during an evening EMH last October and it was mobbed. All the other times we visited Epcot during the evening on that trip were blissfully quiet. Even as an onsite guest, it would take a lot to convince me that I shouldn't avoid EMHs. We are making an exception this August to visit AK during an evening EMH, simply because it will be a rare treat to be at AK during the evening.
EE was always just that - Early Entry (i.e. mornings). Since the advent of EMH (mornings and evenings), I think the evenings have been more popular. I guess that's not really surprising but people are unlikely to be able to burn the candle at both ends, so the mornings are potentially not as busy as they once were. Conventional wisdom has always been to take advantage of the EMH mornings (if you're inclined to do so) and then move to another park once the EMH park starts to become crowded (late morning).
To answer your question directly - the morning EMH parks will be busy all day, the evening ones from lunchtime onwards.
