I'd recommend two days.
One day you would be in a constant rush to try to fulfill everything. If the crowds are light, or average, you can probably do just about everything. However, that is just about everything, as everyone has a different version of "everything". If you wanted to legit do everything in both parks it wouldn't happen at all.
With two days, you would definitely be able to achieve everything you wish to do, or if you legit wanted to do everything in both parks and not have to rush, rush, rush and have more of a relaxing experience.
Also, I do not know when you plan on going so hours are a determining factor as well. If you went during non-peak seasons you have less crowds, but less hours. If you go during peak season, you have higher crowds, but more hours. For example, non-peak hours average 9am-7pm (not including EE) and peak seasons average 9am-10pm.
I want to say that EP isn't like FP. FP has a certain format where you'd be get onto the ride by a more guaranteed specific time, where as EP just guarantees you have a lower wait time. That being said, if it's low, or average crowds you'll get onto attractions much sooner with EP, at most 1/4 of the posted wait time, but most cases are typically much sooner than that. However, it's been reported that during peak seasons when crowds are incredibly high that EP is a sooner wait time, but isn't as quick as it normally is, can be up to half the posted wait time.