Well, I personally prefer Anytime. And the times we've used it we've always told the Maitre D' that we'll sit anywhere he cares to seat us, so we've never waited. Some, who prefer to sit at a table for 2 only, or a table of 4, etc sometime wait. So I guess it depends on how you wish to be seated.
Also, I think if you show up at Peak time you may wait. Personally, if I ever showed up and there was a big line, I'd just put my name in and then go sit and people watch for a while.
The menu is the same as is in the Traditional Dining room.
The Servers will change nightly in Anytime depending on where you are seated. Or, if you wish, you can ask to be put in a particular servers area nightly, thus at least keeping the same server if that is what you wish.
Happy Anniversary and Happy Cruising!!!