Geissele describes the difference pretty succinctly: SSA - "carrot break," SSA-E - "candy cane break." This is very accurate. The former is a bit more gradual, the latter is "right now."
I have owned only the SSA-E, but have shot many rifles with the SSA. I also agree with an earlier assertion that the trigger "shelf" before the stage 2 hammer drop is more pronounced and noticeable in the SSA-E. This makes it easier for me to hold the trigger right at the end of stage 1. I can hold it indefinitely for precision or target work, where breathing control and very fine rifle sight adjustments are needed. It is harder for me to get to that shelf and hold it there while making adjustments with the SSA, although the difference in stage 1 weight between the two triggers is very slight.
The actual difference in perceived weight, on either stage 1 or stage 2 seems less discernible than the shelf detection and the crispness of the final trigger release and hammer drop. The stage two "break" is much lighter, at 1.2 lbs, for the "E" compared to 2.0 pounds for the SSA. This is more noticeable.
That's about as analytical as I can make it. You really need to find someone with each type and give them a try. At least dry fire them.
If all you run is a red dot, you do not need the SSA-E. But if precision shooting with breathing control and fine manipulation of the rifle for long distance shooting or high precision are needed, the "E" is fantastic. Now that I've used the "E" for a couple years, I have no problem also using it for HD. It becomes a matter of muscle memory and being intimately familiar with the rifle. The "E" is not unsafe for HD, but it's benefits would be wasted if HD and CQB tactical work or center of mass shooting at under 100 yards is all the rifle would see.