We cruise out of Galveston often because our whole family is from Texas and Arkansas. We have a long history of cruising with Royal Caribbean because my grandparents started cruising with them back in the 90's and the rest of us sort of followed suit. Given our almost exclusive experience with RCCL, I can't comment too much about how it compares as a cruise line to other cruise lines, but I can let our 20+ years of sailing with Royal tell the story. Always top-notch service and we can't say we've ever been disappointed by them (well, except for a few little things, but that's going to be the case no matter who you sail with).
So now for this particular cruise. We planned this trip for this week because I go to school in Dallas and we have a fall break the first week of October. Galveston is by all means a world-class departure port and it keeps getting better. The time for us from when we arrived at the port to when we were walking up the gangway was no more than 30-45 minutes. For smooth embarkations such as this, I suggest arriving at the port around 10:30-ish for a 4 o'clock departure. By that time, most if not all of the previous week's passengers will have left, but it's earlier than most of your fellow cruisers will have arrived.
The ship itself is nothing short of amazing. It's recently been upgraded and is beautiful, shiny, and has just about everything on board that any of the new megaships have on them. I love being at sea and the whole maritime experience, so Liberty to me is the perfect balance between being large enough to have enough things to do to keep you entertained all week, but not so big that you lose the true oceangoing experience. With that being said, you won't feel the seas on this ship at all. I just enjoy feeling like I'm on a ship and not in another city haha.
Great embarkation port. Not too busy, but not a ghost town by any means
Cozumel is to Caribbean cruises what turkey is to Thanksgiving dinner. I don't think we've been on a Caribbean cruise that didn't go to Cozumel. It's a solid port, but hasn't really changed much.
Beautiful. Clearest water you'll ever see
Falmouth has improved a lot, but it's still pretty small. It looked like they were working on adding things though, so it's got potential.