The differences between the 3DS and Wii U versions of Mario vs. Donkey Kong: Tipping Stars are few and far between, but the 3DS version does feature some differences of note. You can read our thoughts on the Wii U version of the game here.
The 3DS version takes full advantage of the SpotPass and StreetPass functionality of the 3DS' hardware, and by activating these features you'll be able to send and receive custom levels from the workshop without lifting a finger. This is great if you live in a heavily populated area, but those who live away from the hustle and bustle will likely not be able to make the most of this feature.
There's also a notable absence of any 3D visuals, but this is likely less due to laziness and more down to practicality. Because the game is controlled on the touch screen alone, adding 3D would have been a wasted effort, as the top screen rarely displays anything of absolute importance when actually playing the game. It's a pity as this is a title that would look absolutely stunning with some 3D thrown in, but as it stands there's no way this could have been implemented without it being a waste of resources.
The tipping mechanic remains identical to the Wii U version, but despite the cross-buying system the games behave entirely separately. You can easily download any custom levels you have created on the other version as you would any other level, but your stars and progress do not carry over from one version to the other. This isn't really an issue but it may be slightly irritating that you may not have access to all of your unlocked content in the other version from the get-go.
As with the Wii U version, when you buy one iteration you receive a download code for the other - this'll come as a code in North America so, in theory, you'll be able to either use the other copy yourself or share it with another gamer.
When it comes to deciding which version of the game to play, it entirely comes down to personal taste. The Wii U version is slightly more comfortable and easier on the eyes, but the 3DS version does have the enormous advantage of being portable, which will make or break the decision for many people. As far as the core game is concerned however, there is no difference between versions.