Howejustin, I have cruised numerous times on Carnival and several times on RCCL.
There is a difference in the dress between the two. Carnival has relaxed it's dress " codes "
( if it ever had one it never enforced it anyway ).
On Carnival, jeans, a sport coat and collared shirt would probably not even be noticed on "formal" nights.
However, as I said, I do feel there's a difference between RCCL and Carnival when it comes to dressing for dinner. ON RCCL I don't wear a suit nor tux but a sport coat, tie and a pair of khaki or docker type pants fills the bill nicely. I would just sub the khakis for the jeans, wear the sport coat with a tie and you'd be fine.
Just a step up from Carnival--that's all.
I would think you'd enjoy RCCL, especially if you're going on one of the larger Voyager class ships. Happy sails to you !!