Currently own a 360 and would like to get a DS in the future (I planned to buy it soon but with the announcement of the DSi I figured I may as well wait since I don't want to miss out on games which use DSi's camera and whatnot).
The game I'm playing at the moment (see sig) is Fallout 3, great narrative and gameplay so far. The expanses of the world are so vast that I can spend 3 hours exploring a single
tunnel and afterward realise I'm but half-way to my destination. Side quests are lengthy and full of 'meat' too which is great. I've also been playing Fable 2 recently (although after completing it there isn't much incentive to replay so it's sort of collecting dust in the shadow of Fallout 3).
I steer clear of trashy games like Gears of War which require no thought, have no story, and have dialogue written by what I can only hope is a team of football players (grid iron of course). I much prefer games with a deep storyline to get lost in like Mass Effect (which has to be one of - if not the - best games of this generation).
Next game on my 'to get' list is definitely Prince of Persia, I love the artistic theme and need a nice light game to play. There's a sweet looking (and free) pre-order bonus content offer at the moment which comes with all these sexy goodies: