So, as you've probably heard, this game is literally just the Gamecube version of Pikmin, without a single addition or omission. The graphics haven't been updated, none of the changes from Pikmin 2 are included (multiplayer, for example): it is, as the name suggests, Pikmin, with new, Wii-based controls. That said, Pikmin is still an excellent game - among the best on the Gamecube - and if you haven't played it, it's worth a shot.
The main advantage of the Wii controls is that, while running around on the forest floor, the Wii remote aims the reticule for throwing Pikmin, allowing a level of precision to your throws that was not available with the Gamecube's dual-joystick setup. However, in my opinion, the losses outweigh the gains. The camera system takes some getting used to - even in the old game there were problems but the Wiimote makes them even more pronounced. And as the camera's orientation influences the direction of the in-game map, a point that may not be clear at the beginning of the game, but makes sense when you get used to it, this can be troublesome at first. The major problem, though, is that the pikmin themselves are difficult to control. On the Gamecube controller, by using the C-stick, one could direct the Pikmin around Olimar, ordering them to manipulate whatever objects or attack whatever creatures they found in their way. This has been replaced (less effectively) by aiming the Wiimote and pressing the D-pad down, and the results are finicky at best. As a result, while some puzzles and monsters are made easier by the controls (throwing Pikmin at snagrets, for example, is much easier, or aiming at specific objects), others are abysmally difficult (guiding pikmin along a wall or telling them to destroy a gate directly in front of you).
In short, little is gained by the new controls, and you would probably be better off playing the old game if you have a Gamecube controller for your Wii.