I first played Civilisation on our family’s XT PC in the early nineties - you had the option of playing it in 16-colour EGA or 256-Colour VGA; and it ruled a significant part of my childhood...
Turn based strategy certainly isn’t a genre that is over represented on the 360, and while some won’t see that as much of a loss, those who have been initiated into the mysteries of the turn based strategy fandom know that there are few things more rewarding then thinking up a clever strategy and then crushing your opponents without hesitation or mercy...
Back when I got my first DS, the majority of the available games consisted of simple puzzle games, licensed trashed and a few well-polished first-party games...