I have been on both ships, with my last Monarch sailing just this past January. We have had good experiences on both cruiselines, but that was going on the Monarch knowing she is RCI's oldest ship in their fleet.
Since you will probably get more focus on the Dream from these boards (as this is a Disney board!), I will focus on the Monarch and her pros and cons.
Pros
You just cannot beat the price RCI sets for the Monarch. If you time your booking right, you can really get a steal on the cruise cost itself.
The rock climbing wall is an absolute blast! As long as you see good weather during your cruise, the rock climbing wall can be a fun way to kill a few hours in the day.
Less crowded pools. A smaller ship means less passengers, which in turn means fewer folks loading the pools. Plus, the Monarch has fewer children on it; this means the pools aren't as crazy. Yes, the pool does get crowded at times, but I find it better than on the Dream.
Wonderful staff! Yes, Disney really has almost cornered the market on customer service, but the Monarch has a top-notch staff also. They are often ranked among the highest in RCI's fleet, and with good reason. Everyone is pleasant and helpful, and the crew does go out of their way to see you are taken care of.
Some of the daily activities were a blast! Obviously the Belly-flop contest and the Sexiest Man contest were fun. My favorite though was the video scavenger hunt! If they have this on a Monarch sailing, I highly recommend it! An absolute blast!
Embarkation...RCI has this down to a science. It's painless and orderly. Basically, if you are at the port early, once you check-in they seat you...in order...until embarkation. Not a free-for-all.
I must say here, this is a personal huge pro for me. The English Toffee cookies! You can get these up at Sorrento's (pizza counter on the second level of the Windjammer Cafe) or at the Latte-tudes Coffee counter (although at Latte-tudes you will have to purchase a specialty coffee to get one...kind of lame if you ask me...I always just went to Sorrento's).
Cons
The staterooms are small! I mean, really small! If you are looking at an inside stateroom, we are talking about 119 square feet. Unless you decide to look into a junior suite or suite, you will not have a couch in the stateroom. Compare that to Disney, where all staterooms have a seating area. The stateroom size carries over to the bathroom size too. Very small bathrooms.
Obviously the age of the ship is noticeable, but I have to admit RCI does a decent job of keeping the Monarch up. She does show her age, yet it's not like the ship is gross and disgusting! Things just look dated in some areas, and in many areas you will not see the most up-to-date decor and technology.
With the Monarch, you will eat in one set dining room. While that's the norm in the cruise industry, one of the things I love about Disney is the rotational dining, and eating in a different dining room every night! Also, there was something about the lighting in the main dining room that just seemed off. I can't put my finger on it, but it seemed a bit more low-key and crowded (or something!)
The nightly shows will be more Vegas-style revues since this is what Monarch's theatre is built for. You will not see the Broadway style shows as on Disney.
We found the bars to be lacking a bit. Can't put my finger on that one either. The only one we really enjoyed was Boleros. We might have enjoyed the Schooner Lounge more had the casino, where smoking is allowed, not been right next door.
If you are soda drinkers, you will need to purchase sodas or invest in a unlimited soda card. I'm no longer a soda drinker, but when I was this was a big turn-off for me. (To be fair,
DCL used to charge for this also at one time.)
So, embarkation is smooth-sailing, right? Disembarkation can be a nightmare on RCI! Depending on what group for disembarkation you are in, you could be waiting an hour or so just sitting around...in a theatre possibly...dying to get off the ship. Our last cruise we ended up in the second to last disembarkation group, and oy! I thought we would never get off!
Ok, that's it for my pros and cons, but I think it's only fair I cover CocoCay, RCI's private island. I wouldn't consider it a con, but I have to be honest...it doesn't compare to DCL's
Castaway Cay. If you have never been to either, then you most likely will not be disappointed with CocoCay. If you want to do something other than hang out at the beach or walk around the island, you will have to pay for it (except lunch, of course!). But we typically make a day of it doing just those things...sitting on the beach and wandering around.
Hope this helps give you an idea of the Monarch! Which would I pick? Disney in a heartbeat! That doesn't mean I would snub Monarch either. Just know if you choose Monarch, it is a completely different experience than Disney.