I agree with the posters to consider waiting until the baby is older for either line. We went when our youngest was just over one and still refer to it as the cruise from h-e-"double hockey stick". It was on
Royal Caribbean - one thing that added to the negative that we didn't know not having a child in grade school was that it was also over spring break. The pool deck was so crowded that my oldest got kicked in the head multiple times in the shallow end of the pool. We didn't attempt the pools again.
They didn't bring a pack and play until the evening and the cleaning crew had accidentally left the balcony door cracked open. So no nap and hotter than Hades for the first night.
You also don't know how your baby will do. Our 13 month old cried every night though she was a good sleeper at home so we got zero sleep. We speculated after the cruise we thought it was because she was "sea sick"...a little Benadryl may have helped. We spent quite a bit of time in the room trying to stick to the normal nap schedule but with no sleep at night that was sort of off as well.
We booked an Oasis Suite to have tons of room and be able to close the curtain. Then we had a rude lady in her 50's ring our doorbell every night between midnight and 2 am until one night when I opened the door and gave her the business. We ended up canceling an Alaskan cruise that we had gotten a sweetheart price on Royal based on this experience. We next did Royal when the girls were older and grandma came along...had fun hanging out as a bigger family as there aren't many day-time activities for kids on Royal.
If we were to do one line over the other with a baby, I'd pick Disney hands down. Our kids watched the heck out of Disney Junior so the morning dance parties, character breakfast, character meets were all fun...yes they cried up close to characters when young but were excited from a distance. They were made over by the dining staff. The nursery staff seemed much better equipped and interacted with our kids more at that age. It wasn't until 18 months but our oldest was able to sit through the evening Disney shows. Food is much better on Disney. Alcohol is not that expensive either. I want to say the Captain Mai Tai's are around $6.50, which is good for 5 shots of alcohol per drink. So I think $600 for 7-night cruise seems high. I do end up spending more money on souvenirs on Disney as Royal has nothing special for kids that you can't find at a local toy store.
If you do either line consider doing things out of the norm. On Disney we often skip dinner one night and hit the pool with no crowd. Consider bringing a device that can connect to the tv to watch videos. Bring a white noise track and play off your phone to drown out the hallway noise.
Having said all that we were originally loyal to Royal and are diamond members so will likely be our cruise line of choice at retirement some day.