Fair warning, the entire series is a
Widget Series among Widget Series, includes a little ecchi (perverted) bits, and can downright get into WTF territory, especially during the Dating Sim aspect of them, and in some of the creatable items.
Like Edible said, the music is awesome, but you'll likely need to trawl Youtube for the guy doing English translations, since even if you can understand Japanese, you'll also need to understand a second language called Hymmnos (you can see an example of six lines from three songs in the second game in my signature) if you want to get anywhere figuring out how the songs fit the current theme. EXEC_HARMONIUS/. is creepy as fuck.
As for battle mechanics, the first game is a bit like FFX's CTB system. Vanguards and enemies fire off attacks, you can pick attacks at your leisure. Reyvateils (you get one active in the first game) can use songs and attack at will. The items dropped is entirely dependent on how you battle - being tactical and launching more but smaller spells is preferable to just pounding away at the enemy and unleashing a massive strike at the end.
In comparison, the second game is a bit more like... Well, I haven't played too many RPGs with this type of battle system. Battle is separated into two phases, one for each side. During the Player Phase, two Vanguards can attack at will, while two Reyvateils sing one song, which they can release any time during the Player Phase. During the Enemy Phase, the enemies launch a preset number of attacks, that you have to guard against with a sort of rhythm meter. Hit it perfectly, and no damage. Miss completely, and that Vanguard and the Reyvateil behind them get hurt. As the Vanguards launch off attacks, they increase the powers of the Reyvateils behind them, and enough in the right direction can even help you launch off special attacks (even unleash the power of the titular tower, half a world away) and special abilities, such as Replakia.