The movies are not very old at all, they're quite recent. I think once in awhile, they have a non-Disney movie available too.
They often have 'PremEars' which are when they have a new movie that is being released and they show it on the ships first.
On our cruise in January, there were at least 4 or 5 movies that my DW and I wanted to see, 2 we had to 'make time to see' by squeezing them in at late night showings.
So Yes, I'd say don't go to see it in a theatre, it'll be shown on board. You might ask recent cruisers what was shown on their cruise about 3 or 4 weeks before your cruise to be sure though.
hope that helps