The Navy will pick your rate so don't worry about it. EM is the best because you get to stand the roving watch which means you get to hang out with your buddies (and avoid the dorks. No shortage of those.) to make the watch standing somewhat enjoyable. Think about it: Look at some of these posts. Imagine being stuck for 6 hours in a 5X10 room with them talking about their 3rd grade spelling bee, the soccer trophy they won when they were twelve, A school class rank. You see a few of them here...imagine being stuck captive to their renditions? Not pretty.
Plus, as an EM you get to run the throttles, the best watch. Going to flank cavitate, back emergency is pretty cool. get to hear the turbines scream, hear the steam flow rush through the main steam pump, the boat bucking/vibrating as it responds to thrust...operating the electrical board is cool too.... parallelling generators, battery charges, diesel generator. three pretty good watches that are different.
RO watches stink. MM watches stink. EM is the best.
Most of the time its boring. You clean bilges all the time so the engineer officer can look good cuz all he cares about is the command path. Then you train on the same stuff over and over and over. pretty much blows across the board...but EM is the best as far as watches go...
But, time thinking about it is time wasted.