I don't think I'll ever figure out why everybody believes that "The Super Mario Bros. Super Show" was the best of Mario's animated series. That series had too many episodes with the Mario Bros. and their bosom buddies Peach and Toad going to a ridiculous land that usually doesn't exist in the games, only to end up having to save said land from Bowser, and being forced through an out-of-place movie parody while they're at it. Nevertheless, DiC Entertainment made the right choice as to when to release the show ('cause, you know, in 1989, nobody cared how crappy something so long as it featured Mario or the Ninja Turtles), and they managed to get surprisingly high ratings in spite of the dodgy writing and bad animation. So it was only appropriate that they decided to give Nintendo's mascot another run in animation even after they had ended production of the original series.
"The Adventures of Super Mario Bros. 3", shown in an hour-length show with "Captain N"'s second season, is based on the NES game Super Mario Bros. 3, which had been released in Japan in 1988, got big-screen exposure in "The Wizard", and made its way to American store shelves and the hands of over 17 million customers several months prior to this show's premiere. For whatever reason, I'm probably one of the few people who finds this superior to its syndicated predecessor. And you'd think it would be the best, considering that it actually managed to beat "Teenage Mutant Ninja Turtles", whose time slot it shared, in the ratings.
Bowser... um, excuse me, "King Koopa", is back for revenge for his 51 losses in the 52 animated episodes of the previous series (the official descriptions DiC has used in recent years claim that he has escaped from some place called the Banishment Zone, but this is never actually mentioned in the show itself), but instead of mooching minions from Wart, this time he is joined by his seven Koopalings who were introduced in the aforementioned game. Larry, Morton, Wendy, Iggy, Roy, Lemmy, and Ludwig were a lot more prominent in the early half of the 1990s than they appear to be today, showing up only in Mario & Luigi: Superstar Saga and, if the rumors are correct, the forthcoming New Super Mario Bros., and apparently DiC must've thought they'd get to be big characters, to the point that they've decided to give the kids strange nicknames based on their personalities and appearances. At least, I assume they're nicknames. 'Cause if they're not, then somebody screwed up!
Bowser's favorite minions aren't the only changes this show has from the one it followed. In "The SMB Super Show", there didn't seem to be any continuity at all. This time, the writers don't stick the Mario Bros. group into random locations for no apparent reason other than to rip off something that "Tiny Toon Adventures" could've just as easily done. Now, whenever the characters go traveling, they just need to visit the eight worlds featured in Super Mario Bros. 3! Additionally, even though they had less time between the game's release and the show's premiere than they did between SMB2's release and "The Super Show"'s premiere, most of what happens in this show fits in better with the games' continuity; in other words, there aren't as many game-relation errors here. For example, when Bowser flees from Fiery Mario in "A Toadally Magical Adventure", it's obviously in reference to the fact that Bowser is easily beaten by fireballs in the NES games!
So does the show have any problems? Yes, it does. Some people complain that the animation got worse in this series. Given that the animation of "The SMB Super Show" was already lackluster to begin with, I don't really much of a difference. For me, the big problem comes in the gang's semi-weekly trips to Earth. For some reason, they always, ALWAYS refer to it as "the Real World". Does this mean that the characters are aware that they don't actually exist? How do they feel about that? Furthermore, even though the writers seem to have managed to play more of SMB3 than they apparently did with the first two, poorly-written episodes full of plot holes are still around, such as in "Princess Toadstool For President" and "The Ugly Mermaid".
Overall, though, I feel that "The Adventures of SMB3" is the best of the three Super Mario Bros. cartoon shows, or at least the most preferable. I would recommend that new fans of Mario check it out before they see "The Super Show", but there's only one DVD of this show available right now, and it doesn't look like Shout! Factory is interested in giving it the treatment they're giving the original.