Brian,
We've found Princess and RCI to be more alike than different. RCI ships are prettier (more of a WOW factor), service is about the same on both.
As PH said, My Time Dining doesn't have a "surcharge". In order to utilize My Time Dining, you must pre-pay all your tips. You will not be charged a per day fee on your account, as your tips have been prepaid. If you don't want to do MTD, they will still NOT charge your account a fee per day. You will be expected to pay the tips at the end of the cruise. You can, if you wish, put them on your SeaPass account, or you can pay in cash.
We've found the laundry facilities on Princess somewhat convenient, but at times we've spent too much vacation time waiting for a washer or dryer to finish, or waiting to take our clothes out so someone else can use the appliance. Frankly, I've used the laundry, but prefer to pay someone to do the laundry for me....after all, I'm on vacation.
One difference we've found is that unless you book Princess very early, you are almost forced into Personal Choice Dining, as only one dining room is allocated for traditional, and the rest are personal choice. On RCI the MTD spaces are limited, and I haven't heard of anyone having to take MTD when they want traditional. Sometimes MTD is full, so you have to take traditional.
We've found the balcony rooms on RCI to be larger and better laid out than similar rooms on Princess. We have a couch on RCI, and have only had a barrel chair on Princess, which we had to move every time we wanted to access the balcony. We also found the staff on RCI to be friendlier......they knew our names and greeted us by name on the second day. On Princess we found the staff was professional and courteous, but not friendly. Shows on both are pretty much the same. Food is subjective, but we found desserts on Princess better. We liked the setup of the Windjammer better than the set up of the Horizon Court on Princess. Also, the steak house (Chops) on Princess is a million times better than the steak house on Princess (Chops is a separate restaurant, and on Princess they used a blocked off section of the Horizon Court). We did like the afternoon ice cream on Princess, but didn't like the fact that lemonade was not a free drink in Horizon Court (that may have changed, I'm not sure). All in all, one is pretty much like the other, IMO.
Just one more thing, Radiance is a ship with lots of glass, so you will have amazing outside views from all over the ship. We did a Princess cruisetour in Alaska, but next year we are doing a RCI cruisetour...on Radiance!
Rita
Rita