Rather than compare this game to Mario Golf for the Game Boy Color, I think the best approach is to take this game both on its own merits and as a companion to the GameCube Mario Golf. So if you've played Mario Golf for the Game Boy Color, bear with me if I explain aspects of this game as if they were new, even if they aren't.
As a fan of all sorts of golf games, be it Tiger Woods or Golden Tee, I can tell you that the golf game genre is one of the few that isn't lacking in originality. Almost all the good golf games feel different from the rest, and when they don't, they at least look different. I've enjoyed the Tiger Woods series immensely, and though it did take some effort on my part to adjust to the controls in Mario Gold: Toadstool Tour for the GameCube, once I did I had a blast. So, if you own a GameCube and have even a passing interest in golf games, get Toadstool Tour, especially because of its newly reduced price as a Players Choice title.
That being said, anybody who's followed the process Nintendo has been implementing over the past couple years knows that if there's a good Nintendo game made for the GameCube, some sort of GBA compatibility should be expected. Mario Golf: Advance Tour follows in that vein, and the result is a good one.
The first, most obvious difference between Advance Tour and Toadstool Tour is the playable characters. In Toadstool Tour, you can play through the courses as all your favorite Mario Bros. characters, from the mustachioed plumber himself to his girlfriend Peach to his nemesis Bowser. In Advance Tour, the Mario characters do appear in the game, as CPU opponents. You only get to play against them once you've proven you worth against lesser players. You create your own human character to play as, and are assigned a partner. While technically you only control the one character while the other tags along, you are responsible for "raising" both of them.
"Raising?" you ask? Yes, that is the other main difference between this game and its GameCube counterpart: Advance Tour has a RPG story element in addition to the golf gameplay. You will take your characters through the clubhouses and gather golf knowledge from the various characters you meet, which progresses your characters. You also open up new courses as you advance through the story mode, and you can hone your game in practice or in several mini games, such as Club Slots.
As to the GameCube/GBA link cable connectivity aspects of the game, there are two main features. The first is the ability to export your characters from Advance Tour into the GameCube Toadstool Tour game to make them stronger than you would be able to without the transfer. It does appear that Toadstool Tour players can be transferred to Advance Tour, although the Nintendo press release was a little awkwardly phrased in this regard, and therefore the details about this feature are still a little ambiguous. The second main connectivity feature is the unlocking of special courses in Advance Tour by linking up the two games.
The game looks incredible, with the courses being rendered in beautiful 3D. The courses can be viewed as a 2D map as well, like in Toadstool Tour, and the RPG "walking around" parts of the game look very nice, although certainly not revolutionary.
There's also a multiplayer mode that allows for up to four players to link up and hit the links, which should be a blast. Now, for those of you who have heard that Nintendo's new Wireless Adapter is going to be bundled in with the game, well, you're at least half right. Nintendo does plan on including the Wireless Adapater, which allows GBAs to link up without the need cables, but this is only for the Japanese version of Advance Tour as well as Pokemon games. No plans have been announced for similar bundles in the United States. In fact, Nintendo has yet to release details about when and if US gamers will be able to get their hands on one of these adapters. So it's not a "no" but it definitely isn't a "yes."