I agree that where you get your degree from *probably* doesn't matter. Of course, it's a very competitive program and if there's one spot and 10 applicants with the same GPA, great recommendations, evals, etc., I'd imagine they'd go with the "better" degree. But then again, I'm not the one picking the sailors.
However, you have to be hand selected by the admiral to become a nuke officer. If you make it that far, you'll have an interview with him. He's going to ask you some really tough science, engineering, and math questions. If you don't know the answer to those, it doesn't matter where you're degree is from, because he's not going to pick you. If you get a TESC degree with your nuke credits and take a couple extra classes without taking those science, engineering, and math classes, you're not going to make it through your interview. Granted, you can study up on your own, but you're not going to have the time you imagine you will.