I think you need a confidence boost! Honestly, if this school didn't think you were capable of doing the work they wouldn't have accepted you. I'm not sure what your specific application process consisted of, but you likely had to submit grades, a personal statement, resume, recommendations, GRE scores, interview, etc. That's a pretty rigorous process, and when they looked at your total package they felt that you had what it took to succeed in their program. You've got to have a fair amount of trust that they know what they're doing (and judging from their pass rates, it sounds like they do).
That being said, it sounds like your other option is also good... perhaps it doesn't have the prestige, but I think in nursing the name of your school doesn't matter so much, so I don't think you can really go wrong whichever school you choose. Neither program is going to be a walk in the park. In fact, they're probably pretty similar in terms of time commitment even though the other school hasn't given you details.
For my school, they also accept 24 students per class. The professors know us. They want us to succeed. They know we're under a lot of stress. We work together (as a class and as a department) to make sure that we're getting where we need to go. They want their money and they want their good reputation to continue, so they're not going to be letting people fail right and left. If you're willing to put in the time and effort you should be just fine.
Take a deep breath. Think about the two schools and which one you really want to be at. Forget the names or reputations or whatever. Which school gave you the warmer feeling? Which one are you more excited about? Then take the plunge. Congratulations, again!