The DS version is more intuitive and straightforward. The upper screen shows the playfield, while the touch screen has an image of your ship, which you simply circle the stylus around to aim. Out of any Geometry Wars title, this approach is far and away the most intuitive and precise, meaning it's good for novices and pros alike. It's counter-balanced a bit by having to use a D-pad for movement, which can't compare to analog sticks. You also have the option of using the touchpad as the playscreen, and just aiming directly around your ship.
With the "How does it play?" out of the way, the next question is "What's new?" First off, the single infinite stage has been chopped up to make way for an entire interplanetary campaign. You jump around the galaxy in a kind of menu, selecting solar systems, and then picking planets for actual battles. Each battle is different, tweaking enemy types or tactics, playfield shapes, and so on. Neo Classic battles look just like traditional Geometry Wars: Retro Evolved, except with some new enemies. Another exciting arena is a hexagon with a gravity well in the center. The well creates a vortex that spins around within the hexagon, drawing everything - you, enemies, bullets - toward the center. Then after a brief time, the rotation reverses and everything is pushed away from the center.
In keeping with the "don't fix what ain't broke" motif, your own ship never changes. It will always do everything just like you remember from Retro Evolved. However, the same cannot be said for your new wingman, the Drone. It flies alongside you and really doesn't do much initially - but you can fix that. During battles, items called Geoms are now released when you kill enemies. If you pick them up, you can use them to purchase upgrades for your drone or new behaviors it can learn. For instance, it can be taught to gather Geoms for you, to attack enemies, act as a shield (it's indestructible), and so on. Equipping your drone is a part of the strategy, as the designers have intended for one specific drone configuration as the best for a particular battle. You'll want to figure this out, because every battle has its own specific leaderboard.
If you have the Wii version and a DS or know someone who has a DS, you can download the full version of Retro Evolved to any DS. It stays on the DS as long as the power stays on (sleep is fine) or no game cards are inserted. The Wii has its own multiplayer mode, which is Retro Evolved played via co-op. The DS has its own multiplayer mode, although we don't know anything more than that it's called "Simultaneous Multiplayer." Which actually gives us a pretty good idea of what's it's going to be.
Sierra has managed to expand the game enough to make it worth a full-blown purchase, but at the same time succeeded in preserving the fundamentals of the original. Are your thumbs/wrists twitching yet?