Chrono Cross is an interesting game, although it's not what I expected. It has a very unique gameplay style. It uses combination attacks like Xenogears and has what's known as "elements" for magic and special attacks (kinda like materia from FF7). The battle system is rather complex and takes some getting used to though.
The story/plot is very confusing. I've played it over twice and still don't get most of the story. There's not much to link it to the original game, except for some references to Lavos and Chrono now and then. The best way to link it to CT would be Princess Shala. The last time you see her in CT is in the underwater palace in the Kingdom of Zeal. CC expands on her fate after that incident. It's an intriguing plot though, filled with interesting scenarios and many touching moments. It's worth checking out at least.
The game follows in the tradition of CT, with awesome graphics and soundtrack. It's known to have one of the best soundtrack in any RPG on the PSX and its graphical effects are top-notch.
It's a decent game for the most part but there's one elements I found especially bad and it's the numerous, repetitive, blank-slate characters. The game has dozens and dozens of characters, possible the largest cast of characters in any RPG to date. Only a couple of them are really important to the story and most of them you have the option of recruiting. The characters are very generic though, they only have a few unique abilities and the rest of their abilities you fill in. This is a huge change from CT, which had only a handful of characters but they were all unique and had different abilities. The best way to compare it would be Final Fantasy 8. The character's abilities were almost solely determined by junctions and it almost the same scenario with CC; the elements you put on a characters determine their abilities. I didn't like this system at all and it spoiled the game for me.
