Back when I was playing Tekken 2, the depth of the game was astonishing, and the same applies to Tag Tournament. Each of the 30-odd characters has its own martial arts style based on reality, with some admittedly outrageous tweaks. This means you can create everyone's fantasy martial arts movie by staging battles pitting endless combinations of combatants: Sumo vs. (Space) Samurai, Thai Boxing vs. Tae Kwon Do, Kangaroo vs. Bear, etc.
Each character has one hundred or so moves of its own, the more outrageous of which require complex combinations of button pushing. This gives you the incentive to rehearse using the practice screen, but you can also get away with mashing the buttons and seeing what comes up. At some point you may wonder if the time spent learning these neat tricks could have been better used learning the real martial art. But you would have to get out of the house to do that.
While the graphics are vastly improved over the previous Tekkens, given that the gameplay remains basically the same, I can't see much advantage over owning a previous version. They all offer near infinite replayability. And frankly, Tekken 2 had a much better practice area — a key element to mastering the game. Tekken Tag's practice has eliminated some basic help, such as displaying the key combinations you are pushing and assigning musical notes to the keys.
Most disappointing, they still haven't integrated the use of the left thumb-stick, which would make the game much easier. The arcade version uses a stick, so why not the home version? Beats me. That would have been the "must-have" difference.
Bottom line: If you don't own any of the Tekken series, get one. If you are big on graphics, get Tekken Tag Tournament. If you are budget-conscious or a cheapskate, get a used copy of Tekken 2 or 3 and enjoy.