I can comment about ABET v. Non-ABET with respect to hiring in the non-nuke Engineering field. The answer is that ABET is preferred, but non-ABET, can be acceptable, depending on school. So, in essence, as long as it's not degree mill type place and is Regionally accredited, it will be acceptable.
This has changed somewhat in the last few years. Up until about 3 or 4 years ago we wouldn't accept non-ABET engineering degrees for our Engineers positions, but would accept them for our Tech positions.
In general once you graduate, it doesn't matter if you went to University of Washington or MIT, or Podunk U. The 'sheep skin' is what matters. Even then it's just to get you in the door. You can have a guy with an MIT degree, but if he's not otherwise qualified for the job... circular file. I've hired for a number of positions in my company. I've had guys with degrees from Ivy League schools apply, and rejected them just as fast. Don't have the skills needed for the job, that fancy schmancy Ivy League diploma isn't going to pull you out. It's not even a tie breaker really.
A diploma isn't a meal ticket, it's just a qualifier to get you in the door. I really wish more people would understand that.