Well, as with most things about cruising, it really does depend on the cruise line and ship as to who dresses up and who doesn't. We're taking our grandson on a Carnival cruise in three weeks and he's already talking about wearing his 'suit' for dinner! So I guess we'll be dressing accordingly since he wants to make it special. But normally on a Carnival cruise, I never wear a suit. A tie is about as fancy as I'll go. Then again, on a Celebrity cruise I pretty much am required to wear at the minimum a sport coat if not a suit.
Personally, I'm one of those who really don't want to get all dressed up - I'm on vacation! And unlike many people, as soon as dinner is done, so are my 'dress up' clothes.
So yes, I can see where on some cruise it's us old timers who prefer to dress down instead of dressing up.
As for the type of service we've gotten, usually we don't see too much of a difference between traditional seating or anytime dining, except with traditional dining the waitstaff gets to know you, what you like, what you don't like, etc, so they are sometimes more attentive to your needs and will often anticipate how bests to serve you.