They're very hard to compare, as the Wii is a console, and the DSi is a portable system.
The DSi would be a good choice for someone who doesn't spend a lot of time at home, and wants to play games on the go.
The Wii, however, would be the better choice for most people. More engaging/in depth games, the motion controls would definitely be fun, as well as the relatively low price tag. The Wii only costs about $30 more than the DSi, the last time I checked.
