Are you talking about the new grad fellowships which are basically a contracted, full-time permanent position or some sort of internship-type position?
I applied for a NICU fellowship position just prior to graduation and at the last minute when they finally made their decisions, was not hired there. I did do a med/surg-type fellowship where I was hired for a full-time position on a floor.
Pros: It is good training and can be intense. It is full-time with benefits and you can make some close friendships while they review many topics from school (basics like diabetes, IVs, etc.) and moving into the more narrow topics for your specialty.
Cons: If you don't like your floor/position/job/hours, whatever, you will find that once you sign their fellowship contract, you are indebted to them if you leave prior to two years of fulfillment. Additionally, they will ding you for whatever portion of your "sign-on" bonus (if they're still even offering those). They do prorate the fellowship contract based on hours already worked. And they WILL come after you for it. With the threat of a collections suit if you don't work with them.
I think St. John's was a pretty good place to work as hospitals go. I would've preferred a NICU position, but such is life. I do know that friends who are there are complaining about the shortage of staff these days with all the cutbacks. In the specialty units you may wait YEARS to get on a day shift. Since jobs are a bit harder to come by right now, I don't think you'll find a lot of coddling. You will work when they want, how they want.
Bedside nursing is the toughest thing I have ever done. The pay is not nearly enough for what nurses go through and the expectations there are. I will never be sorry I went to nursing school as I learned so much about myself and life, and made some lifelong friends, but I honestly would want someone contemplating the field to truly think about their reasons for doing so.
But then you didn't ask about that, lol. Truly make sure you know what you're getting in to before signing anything -- and best wishes!!