Had both, though I got the DS fairly late.  Got a Wii as soon as I could find one in 2007.  Got a DS in 2009, over 5 years after it came out, because of a scheduling quirk at the end of the school year where I had a lot of free time and nothing to do but sit around the cafeteria for much of the day.  If my memory is correct, it was my father's idea.  At the very least, because of how absurd my schedule was, he was much more willing to buy the DS for me than he was with the Gamecube I had to beg for in 2003.  If not for that I probably never would have gotten a DS.

Got both at launch. 04 and 06 respectively. Though I played DS way more than Wii. No More Heroes is still my favorite game between the two platforms.