PSP was the better hardware by far. I still say the dual screens is a stupid design, just do one screen! Everybody only ever looked at the top screen unless there was some dumb gimmick that made you try and hold a stylus and push buttons at the same time... however, the DS was by far the better supported system with games so it wins, even though it is a stupid design...
When you play a game where you switch between menus, a second screen where the menu is always visible is a godsend. This is the case with Chrono Trigger on the DS, which still is imo the best version of all.