If you win a bid for move up you retain the perks you had such as internet, tips, beverage package. You do not get AI unless you had it originally. You will get amenities of the new room. So a move up to Aqua gives you Blu and other amenities of room. A move up to a suite will give you Luminae, The Retreat and could be more depending on what suite you get. You get the Captains Club Points of your original room. If the move up to a higher category increases the daily tips you will be charged the tips of the new room. If you already have tips included with original booking you will pay the difference in tips.
Also, once you win a move up you cannot refuse the room, so it may not always be a better room.
On our cruise in April it was cheaper for us to upgrade than to do a move up. Hope this helps.