Even though it isn't a huge improvement over Tekken 3, Tekken 4 is still an incredible fighting game.
Other than the original Tekken, Tekken 4 is popularly considered by fans to be one of the worst in the series. Personally, I think Tekken 4 could've been better than it was, but it was still the best fighting game on the PS2 at the time, edging out Virtua Fighter 4 in my opinion. A lot of people will disagree with that, but just being on the same level as Virtua Fighter 4 should tell you something about how great Tekken 4 is.
The first immediate difference you'll see in Tekken 4 compared to the past games are the visuals. I usually don't talk in depth about graphics because they're not that important to me. But damn, Tekken 4 looked incredible back then, and I think the visuals still hold up today. Particularly the character models. They're some of the most realistic and beautiful character models you'll see. Maybe this is just me, but I don't think this game will ever lose its luster. I've played the PS3 and 360, but I still believe this old PS2 game looks fantastic.
The only aspect of the visuals I don't like is Heihachi's costume. It's a little too, "revealing" for my tastes. Let's just say, he's got some chiseled butt cheeks for such an old man.
The problem is, other than the visuals, there really aren't too many big improvements on the Tekken formula to be found here. The gameplay feels pretty much identical. I mean, after Tekken 3, there really isn't a way to make it more fun or more smooth. The developers mostly concentrated on the levels you fight in. In previous Tekken games, it was just a flat floor with a static background. But in Tekken 4, it's an actual level, and they have walls and sometimes different elevations in the floor.
Even though it's more realistic, this feature was the one most players cited as the reason Tekken 4 wasn't as good. The environment has a big influence on the fight now. Sometimes, you can trap your opponent up against a wall and just beat the crap out of them. Sometimes, you can be completely defenseless when trapped against a wall. As for the elevations in the floor. Again, they're more realistic. But, they give an unfair advantage if one person is fighting on ground level and the other is fighting on a higher part. It gives an unfair advantage to the lower player because it makes the higher player easier to hit.
None of this stuff cripples the game, and I think a lot of reviewers overexaggerated the effect it has on the game. It can lead to a few cheap fights, though.
Another thing the developers could've improved more is the roster. Tekken 3 had 15 new characters. But Tekken 4 only has three new characters. One of whom, Christie Montiero, has an identical moveset to Eddy Gordo (Eddy himself is actually an alternate costume for Christie). The only two completely new characters are Steve Fox and Craig Marduk. I like both of them. Steve is interesting because he's a boxer, and he doesn't have any kick attacks. The kick buttons instead do ducking and weaving-type moves, which can be used to make more powerful punches. Marduk is huge. He's a big dude. He's powerful too. He's a Vale Tudo fighter. To make up for this, Jin Kazama has an almost completely new moveset, as he "unlearned" the Mishima style he was raised on and learned traditional Karate instead.
Good stuff, but I would've liked to have more new characters, or have more of the Tekken 2 characters who weren't in Tekken 3 to return. Kazuya Mishima is back, but others like Baek Doo San and Bruce Irving are still missing. Most of the characters are returning from Tekken 3.
Tekken Force mode, the beat-em-up minigame from Tekken 3, returns in Tekken 4, but it's pretty different in Tekken 4. Instead of a side-scroller, it's a behind the back view. I think it's an improvement over Tekken 3's mode, but that's not saying much. It's a decent add-on, but it's not good enough to be a main attraction. It's a nice distraction.
Overall, the visuals are a huge improvement, but the gameplay and roster are pretty much directly lifted from Tekken 3 with only minor enhancements. Even though it isn't a huge improvement over Tekken 3, Tekken 4 is still an incredible fighting game. I played it for hours and had a great time.