^I've actually been replaying the DBZ 1-3 games lately and I have this to say:
I think that Dragon Ball Z Budokai has some of the best cinematic sequences on the planet. Seriously, it makes you feel as if you're actually watching the show, and more, it has a gripping narrative, great writing, and is only hindered by its length, it's age (if it had been current generation, or at least not 2001-3, it could have done a lot more) and somewhat bland gameplay (it got fleshed out in two, and further in three, but it was still fun). The cinematic and the presentation are just plain astounding, especially for the time; you could feel the anger in the characters, the power of their attacks, and you would be emotionally affected with suspense or fear when the cinematics segue into fights. It's that that makes me truly love the Story Mode in DBZ (oddly enough, when upscaled 4x+ it's revealed that it also has the greatest graphics of the three games, as well as the tenkaichi titles.
Dragon Ball Z Budokai 2, I've never heard anyone knock on the story mode, but that's really what takes me back to it. It's one of the most unique and most inventive story modes in a fighting game, and it was a very bold move on their part. It turns the game into a sort of strategy game, and do to the different events, possibilities, and unlockables, it has high replay value. Then there's the gameplay. It has more moves, and some moves that were previously clones were made their own moves. Plus, the game had more characters and some non-canonical characters thrown in for fun, as well as the introduction of the fusion and absorption systems, and most importantly, button input in various moves (and cel-shaded graphics, which carried into Budokai 3). Dragon Ball Z Budokai 2 will forever hold its place as one of my favorite fighting games in existence.
Budokai 3, this game completely fleshed out the fighting aspects of the Budokai series. It made it so that fighting wasn't so reliant on skills, that way you wouldn't be out of the game if you only had one or two, or no skills. It added teleportation (so to speak), Burst Mode (if that's what it's called), Power Struggles (Honestly, my favorite addition), dodging, and it dismissed most of the replica moves and made them their own. It also added some GT characters without making a GT saga (probably due to the show's low fan reception but SSJ4's high fan reception) and added a few movie characters (most notably, Broly). Sadly, it removed the "analog stick rotation" input and replaced it with a timed button input. Conversely, it was very pretty, and even if Budokai 1 had the best graphics technologically, 3 had the best looking in art style and improvements. It's Story Mode was great, from my PoV, and due to it's being so different from 2's, I don't really compare the two, I just say "play both". It was nonlinear and had a crapton of unlockables, as well as rewards for doing actions done in the show. It also had different endings and different paths, plus the addition of free-movement allowed for a lot of possibilities that they exploited and did well.
...So I guess I'm saying that I don't really think 2 was underrated, but if only because I've never heard of bad reception for it's story (I've heard mostly positive reception).