Tending to your garden and interacting with the characters will be done through the DS touchscreen. Rare is saying that "it's the same game". According to a Rare Employee on their forums, the game won't have the same 360 graphics, but the DS team has gotten "most of the features from the original into the DS version".
It will be created by the same team as the 360 version and the graphics will be "beautiful" and the game will be coming soon. No word yet on if you'll be able to mail friends items through Wi-Fi, but I imagine they would set that up like they do for Animal crossing's mail system.