MARKETABILITY:
The DS has to go neck to neck with the PSP. Average Consumer Joe wouldn't take the DS as serious if it's games came in (perceived) cheap, cardboard boxes. (Read: Nintendo doesn't want the perception that the DS is just another Gameboy.)
"Heck, PSP games come in DVD-like cases... DS games come in them too. Hmmmmmmmm... Decisions."
For the more informed lot, it wouldn't matter, cardboard or plastic.
However, I prefer plastic as it makes for a nicer display piece. Yeah, I'm OCD like that -- my inner-collector at work. I mean, if DVDs and PSP games get the treatment...
Euroland DS cases are thicker to accomodate multiple languages if I'm not mistaken.
North American Gamecube cases came in standard size as it would frustrate the consumers over here in the U.S.A., Canada, and Mexico if they couldn't put their games in the same storage rack as other platform games and DVD movies. Japan, however, seeing that the 3 inch media is physically smaller, "necessitates" smaller packaging (smaller country, space is a premium, etc.) This doesn't carry over to the DS due to it being region free.