We have stayed at both the Nick Hotel and the Swan/Dolphin. My kids ABSOLUTELY preferred the Nick Hotel. The pool complex is amazing. And it was a blast for all of us adults too (we felt like kids again!). My kids are 11 and 8. Nick also had 'slime time' where everyone can get slimed (green tinted water) at the pool every night. The rooms were great too, since the kids had their own room and space to hang out, a little kitchenette and a separate bedroom for us.
All that said, my kids enjoyed the pool at the Swan, but they enjoy the pools at every hotel.
If it is a vacation all about the kids, Nick Hotel has it all over Swan. If you are looking to please the adults more, then I recommend the Swan (nicer hotel overall with more food options and the boardwalk nearby is a big plus).
The Nick is just one of those hotels I think everyone should try once with their kids. You will all play together and it is so much fun. It is so large that we never felt crowded. Maybe you could split your stay?