My husband and I have sailed with Celebrity 5 times - we are taking our 6th in April. We have found that anything goes during the day. Shorts & T's are the standard - swim suit & cover-up or sarong is the other for women. If you wish to attend wine tastings, they prefer you to be in dressier wear (dress short with polo); otherwise around the pool, it's casual. Dinners are dressier - men wear long pants with shirt or polo - some wear blazers. With luggage restrictions on aircrafts, dress pants & polos for men is sufficient and tux or dark suit for formal nights as Cruise Fanatic has indicated. It's a little easier for women - our outfits are lighter in weight and can be crammed in a suitcase
Celebrity always has that extra touch - when boarding they do in style with spark. wine / when in port you are welcomed back with cold towels and refreshments. On deck on sea days, they parade w/iced face towels.
We have been on RCI & Holland of America as well. Celebrity provides extra special touches.
Enjoy your holiday whichever cruise line that you select.