DDS2 has the gameplay as DDS1 at heart, but there are some noteworthy differences about it:
For starters, Dungeon design is so much less frustrating. Less Pitfall bullshit, for example.
Enemies have less Hax Bullshit then before, so simply going 2nd isn't as painful as it was in the first game where you could just get status raped before doing anything (this is especially good cause Cielo is a forced PC for an actual lengthy dungeon; no, he's not much better than he was in the first game, but the existence of less status whoring makes him far less a liability to your overall team.)
Existence of Half Transformation battles; basically, you start some fights half transformed. You can use nothing but Physicals, and you take more damage, but your physicals do lots more damage, ignore all form of resists, and your crit rate is obscene (though your hit rate is lowered, so 90% of your successful hits will be Critical hits anyway); you also get double the EXP when you win fights like these. This is a double edged sword, as its a neat addition to the game, but at the same time, can get irksome cause it has obvious downsides and can lead to you getting screwed, and there's no real way to control it IIRC.
Actual plot; DDS1 was nothing more than leading up to DDS2 which has actual plot. I'm not saying the plot is anything spectacular or amazing, just that it actually exists on a level more than "hur hur we're fighting a war, and eating things."
Completely revamped Mantra Grid. Its got the same "get mantra, now you move on" thing as DDS1, except its now more open; one mantra opens up all ones adjacent, as its on this big grid thing. I'd use FF12 License Board as a parallel, but I don't think you've played that. I guess...well, some Mantras had branch offs into two areas? Its like that over the entire board, and you can actually take different routes to the same skills.
Furthermore, there's locked nodes that if you unlock all nodes around it with your SUM TOTAL of your team, then you get a bonus, and said bonus is universal to your entire team as well; this can range to stat boosts to...well, I think its just a permanent stat boost for the most part.
I think DDS2 also invented actual accessories to equip, and a bit of a system around those? It was something else to help raise characters rather than just "Skills and Levels, and upgrading weapons which are useless 90% of the time!"
Lastly, the "Get EXP while inactive" ability is gotten so much earlier, and makes having to swap characters a lot less painful as its far less likely a character is going to be underleveled.
All these factors may not seem major, but they do add up; I'm not going to say "DDS2 is a fantastic game!" but I did feel it was significantly better than DDS1, despite being the same general game at core.
