I will attemt it as nonbiased as possible. Keep in mind my only experience is submarines. I will try and generalize it as much as possible.
MM-
AKA Machinist Mate, or Mechanic.
Mechanics for the most, will work and stand watch in the Engine Room. On watch they operate, monitor, and maintain the propulsion train and associated systems. These include but are not limited to: Main Engines, Turbine Generators, Distilling Plants, Reduction Gears, Sea Water Systems, Hydraulic Plants, Lube Oil Systems, Main Condensers, Lube Oil Purifiers, Various Pumps, Main Feed, Main Steam. They also are responsible for the upkeep of theese system. There are some systems associated with Reactor stuff I left out because I am not too sure if it is appropriate to post it here. They also do maintenance, corrective and preventative on Mechanical systems and Equipment. It Is a job that if you like toying with car engines and tractor parts, you might enjoy.
-ELT
AKA Engineering Laboratory Technician
They are a mechanic, but spend a large portion of there time maintaining Chemistry in the Reactor and steam systems. There is a great folder with may responses to what an ELT is in one of the Navy forums here.
-EM
AKA Electricians Mate, Electrician
They Maintain and operate the equipment used for power generation and distribution. They do thigs from changing lightbulbs, to rewiring complex components. They operate maintain, the battery, the generators(turbine, motor, and diesel), and the cabinets and other equipment used in power distribution. This is no easy job. They own the electrical part of pumps fans and other stuff including the ice cream machine. Which means they own a lot of electrical stuff outside of the engineroom. This too can be a dirty job at times, mostly carbon dust. Some would argue wether or not it is a tough job. I am a MM, who stood a few electrical watches, In my humble opinion EM can be the hardest job on the boat at times. If you liked tearing apart electrical toys and puting them back together, or rewiring fans and outlets at home, you would probably like this job.
-ET
AKA Electronics Technician
There schooling is the longest. Everyone goes to a school, power school and prototype. Power school and prototype are both six months. A school for MMs used to be three months for EMs, slightly longer, and for ETs six months. O most ETs have two years in the Navy before they ever get to a boat. ETs Operate and maintain the electrical systems for reactor safety and operation. A mlot of ET maintenance require the boat to be at sea. So, in port there is not nuch to do except stand duty. ETs usually have the worst duty rotation in port due to manning and qualifications(not always the case, I hear on surface ships it is better). Underway for sumbarine ETs can be very busy. Depending again on manning and qualifications, and the maintenance that needs to be done. It is a relatively cleaner job. If you liked soldering circuit cards, digital eltectronics and such, then you would most likely enjoy this job.
I hope this was helpfull. It is hard to go into too much detail due to classification, submarine only experience, and me being a proud knuckle dragging redneck mechanic.
John