Wait I thought you were in the market for such things. The lite deluxe is the best model of EZ4 out there (it has more memory to run GBA roms from allowing for some niceties there) and is the only one with a working browser patch (although homebrew browsers are better).
General idea
Originally we only had GBA cards and due to some poor security they could be used to run DS code. Tjey could always run GBA code though (indeed no efforts were ever made to prevent it GBA carts from working).
However DS code from GBA slot devices could not be achieved without special measures and the three that were ultimately came in three fashions
1) Passme. These were custom devices that sat in the DS slot and tricked the DS into launching from the DS cart by piggybacking on an official cart. Later blocked and replaced with the passme 2 and succeeded by the nopass (which ultimately turned into straight DS flash cards and also what caused the GBA slot stuff like the EZ4 to not be updated any more). Most DS slot flash carts, at least for a while, included the to ability to launch the GBA slot in DS mode but some have since dropped it or had it error out and not bothered to fix it.
2) Wifime. Later blocked and although extremely impressive not half as nice to use as the likes of the other two in this list.
3) Flashme (
http://home.comcast.net/~olimar/flashme/ ). A replacement firmware for the entire DS but the kicker was you needed to run DS code at least once (to run the install program) or fiddle with some hardware (I do not think anybody ever installed it via hardware that did not have to).
The EZ4 GBA loader ignores anything with the extension .nds (instead only showing .gba and .bin although note the DS homebrew "format" .ds.gba and some use .bin as well will show but will not function in GBA mode).
Again though forget DS stuff from the EZ4 and just buy a DS slot (aka slot1) flash cart as it is less hassle and ultimately makes for a better time. An Acekard 2, supercard DS one or EZ5i are not that expensive and will sort things quite nicely for you and if you want to get a bit more exotic there are some other DS carts.