The DS doesn't have Dolby Headphone, which can make a difference whilst gaming. It depends on how much you use headphones, if you rarely used them for gaming, you probably won't miss it.
The DX/D1 would be a better buy, one, if you used headphones more for gaming, and two, if you had 5.1 speakers. The DX/D1 has technologies to upmix sound to 5.1, which will work well for games with only 2 channel sound for eg.