More fun will be had by the TR audience, but this is still a very, very solid platformer.
Now, naturally, the only remakes anyone cares about are the ones of games they loved and possibly grew up with. And I'm confident that the Tomb Raider audience is okay with me speaking for them and saying Anniversary has done this series a lot of justice.
The main focus of the creation of this game, if you ask me, was to recreate the environments from TR1 and make them all as big and awesome as we all remember. When the city of Vilcabamba emerges from the fog, or when you gaze down the depths of Saint Francis' Folly, the amazing mood and scale of Anniversary once again give you such a sense of discovery. Nothing is merely regurgitated from the original; it's as if Crystal D looked into your mind and designed these levels based on your awe-induced memories of the original. To make things better, the environmental puzzles and paths, taking advantage of the Tomb Raider Legend engine, have been completely revamped to keep you on your toes. You really are experiencing Tomb Raider all over again.
The main issue with modern platformers like Prince of Persia or TMNT is that because of so much time put into level design, the games fall short in length. I'll admit, Anniversary was hit with this issue as well, though it isn't as short as Legend. What's better is the efforts that were taken to add replay to the game. Difficulty levels and time attack modes will have you working for unlockables from about 10 alternate costumes to the instant-killing "golden shotgun." But above all these is hands-down one of the most ingenious ideas I've ever come across in a video game: a commentary. After your first playthrough, you can choose to turn on visible markers hovering in certain points throughout the game which you can touch to activate a playback of the developers talking about making that particular area of TR1 and about recreating it this time around. Since this game was made for the fans, it's definitely worth playing several more times just for this.
I'll also note that since Tomb Raider Legend, a new combat move has been added. The adrenaline dodge allows you to roll away from a lunging opponent, beginning a short "bullet-time" sequence where two cross-hairs fade in from either side of the screen. Holding your fire until the reticles meet at the target means an instant kill for most minor foes, and it adds a not-too-difficult but very fun layer to some decent combat.
When you add great graphics, sound and presentation, a well-done complete remake of a classic and memorable title is well worth the $30 for any TR fan, or even a platformer fan.