The "Deluxe" version added quality-of-life improvements, such as the ability to play as Luigi from the start (rather than beating the game first) and the removal of the "Boost Mode" (which used the GamePad).
For those interested in the technical aspects of the game, New Super Mario Bros. U Deluxe para Switch NSP D Full refers to the game's file format and compatibility. NSP stands for "NSP file format", which is a container format used by Nintendo for digital distribution of games on the Nintendo Switch. D Full refers to the game's complete and full version, which includes all the content and updates. new super mario bros u deluxe para switch nsp d full