My advice to anyone is to be a nuke because you like being a technician/mechanic, are interested in nuclear power, and want to serve your country. If you're doing it for education benefits and whatnot, generally the same opportunities exist for you regardless of where you serve in the military -- you will get out, use the GI bill, go to college and major in something you want to do (which will count much more than your military service anyway), do some internships if necessary, and get a good paying job. Taking the hard route and going nuke for this purpose isn't going to net you too many brownie points unless you're looking to work at a support facility. Quite honestly, you could work half the hours as a STS/STG (sonar technician), do maintenance/diagnostics on more modern computers than the nuke plant has, and still get the same post-Navy educational benefits. The difference is you'll start boot camp as an E-1 instead of an E-3, but there's a LOT of work to go along with the boost in initial paygrade (and not a whole lot of respect to go with it, at least on submarines). So before you undertake the grueling lifestyle of a nuke, make sure that you want it for the sake of being a nuke. Many employers will look at military service all the same because they simply don't know what it entails and don't care to find out. "Oh you were on a submarine? That's cool. Must be tough in all those tight spaces, huh?" is the most in-depth conversation you'll have about what you did in the Navy. They will stereotype you based on your service (hard-working, reliable, disciplined) even if you are an FT (they do almost no maintenance whatsoever and stand watch at a computer). Universities, even technical ones, aren't going to welcome you with open-arms because you were a nuke; they will look at your high school GPA, coursework, SAT scores, and essays like every other applicant, and put you in the "non-traditional applicant" pile next to Marines, Soldiers, Airmen, and Sailors of all ratings and that 30 year old who was working for 10 years before he applied to college.
At sea:
Watch as a nuke will be relatively benign most of the time. As a mechanic, you will start in engineroom lower level where you will take hourly readings on equipment and stay on top of the vast amount of oil leaks all over the place (bonus if you can fix said leaks). In other words, the majority of your time will be spent cleaning equipment, often in hard-to-reach places. You eventually move to ERUL which has a bit less cleaning to do and more direct access to operating vital machinery, and eventually ERS where you supervise ERLL/ERUL and assist when needed.
As a wire rate you start by taking hourly readings on electronic equipment/motors and move into maneuvering where you sit and monitor panels for 6 hours. During deployment these panels will not change unless there is an issue, so the daily routine can be mentally draining.
During workup/inspection periods, you will do a lot of drills. To me, these were fun as you actually got to operate the plant and see how things work. But, it comes at a price -- you will have little free time on a sub when you are doing this and what little free time you do have will be spent sleeping.
During deployment you will have a lot more free time to do stuff because you won't be doing as many drills. You'll do an after-watch cleanup, do whatever PMS has to get done (typically very simple), and then have 3-4 hours of down time before your oncoming time starts. This is where the motivated nukes got into really good shape and the lazier ones just went to the rack and watched porn on their ipads.
You will have little to no involvement with the mission/tactical operations of the ship in subs or surface, so if you're looking for that then you don't want to be a nuke. The AEA and ERS used to do some tactical stuff, but the newer combat systems have automated what they used to do. This wears down on a lot of people mentally because there is no real "payoff" to doing your job -- you are the department that makes the boat go. If the boat goes, no one really cares about you until inspection time. If the boat doesn't go, they're on your ass to make it go again.
In port:
On a sub, you will be in a 3-section duty rotation at least 90% of your time on board the ship. If you are an ET you can look forward to port and starboard SRO watch rotations on some of those duty days. You will work longer hours in-port than any other rating because the Navy will expect you to fix your own equipment (at least if you are on an SSN, I don't know how SSBNs work), and because regulatory agencies put in strict pre-maintenance guidelines that must be followed (ie, more paperwork, more in-depth briefs, walkthroughs, etc) which adds to the time it takes for you to do your job because there is only one EDO and EDPO to go around. It is not uncommon for lines to form outside of maneuvering because of all the briefs that must occur prior to starting work, and the EDO has to conduct these briefs while also tracking procedures and EDPO has to directly supervise any primary plant operations as they occur, unlike the "cone" where the SDO gives an order and divisional leadership is responsible for the conduct and supervision of the evolution. You have to do this while still meeting the same training requirements as if you were at sea (lectures, monitored evolutions, etc). In-port life is arguably the most difficult as a nuke. Mentally, liberty is there, but you have so much work to do and so much red tape to cut through to do it that you just don't get a whole lot of time off.