To those wondering what the DS port of Chrono Trigger has extra, but are too lazy to look themselves: free poster of the box art *only for the first run*, two extra dungeons; the Lost Sanctum which is discovered during the main quest and the Dimensional Vortex accessible after defeating the end boss, some new items and equipment, new script translation (some good some bad), and touch screen functionality. The FMVs from the PSX version are intact as well as a bestiary, item list, tech list, art gallery, music box, and two areas of the Extras menu I haven't unlocked yet (and am too lazy to look for right now).
Also included is the Arena of the Ages, accessible through the main menu or through a certain time nexus within the game. The Arena is a separate component from the main game that allows you to get different items and pieces of equipment earlier than you normally would by "raising" a monster and battling it against an NPC opponent. This is not Monster Rancher as far as depth goes, you don't get to choose a monster at the start, but you do get to choose it's elemental attribute (Light, Shadow, Fire or Water), and you can send it to train in one of any of the areas of time you've been to so far as well as sending one of the 8 arena items with it. Both the time you send it to and the item you send with it influences how its stats are altered, they can be raised, lowered or stay the same, the monster can also learn a new tech, change classes (evolve), or change its elemental type. There's two ways for your monster to fight, in a prize match against an NPC ranging from Tier 1 to 6, the higher the tier is the more powerful your opponent usually is, as well as drawing off of a different reward list. Or there is an Interdimensional match, which competes your monster against another player's through the DS's wireless connection (no clue if this works over WiFi, haven't tried).
Graphics look great, everything is crisp and clear, if not a little small if you're used to playing the SNES or PSX version, a small font can be hard to read at times, but it's not a big deal. The game sounds great as well, I'd compare it to the SNES or PSX versions but it's been too long since I've played the PSX release, and I've only emulated the SNES one. While walking around the top screen shows Crono and friends, as well as the world while the touch screen has a map which is automatically filled in for areas such as towns, but fills in as you explore while in dungeons and other hostile areas. The touch screen also contains "shortcut keys" which lead to either the player menu or each sub-menu connected to it (item screen, equipment, techs, bestiary, etc.) and can be rearranged from the configuration menu. Combat can either be played through the classic menu style with Crono, friends and enemies on the top screen as well as your parties hp, mp, ATB bars, and command menu, while the bottom screen lists the names of the enemies in battle, and can only be controlled with the D-pad and AB buttons. The DS battle style on the other hand moves the teams info to the touch screen as well as their command menus, it also shows the names of the enemies on the touch screen and if you enable it in the configuration menu each of your party members HP and ATB bars hover below their sprite on the top screen. The DS battle style allows you to control combat with either the stylus or D-pad + AB, and is a lot easier to read.
That's most of the info I can give seeing as I just got to the Future ~30 minutes ago. If anyone wants more info about the Arena... hopefully I'll remember to check this thread heh, or PM me.
tl;dr If you've already played it, but want to play it again, instant buy, although I have heard that the new dungeons aren't great... especially the Lost Sanctum. To those that haven't played it but love JRPGs... again (in my opinion at least) instant buy. The graphics, sound, gameplay, story and controls are all great, and the Arena of Ages provides a nice distraction from the main game while netting you more powerful gear earlier on.