Ds games aren't regionlocked on the 3ds as far as I know, only dsiware and 3ds games.
Both games are pretty similar, but Days of Ruin has a darker atmosphere and is more balanced, at the price of some character variety. Dual Strike has characters with bonuses and powers centered around cities, roads, non-infantry non-artillery land units, sea units, for example. And powers/superpowers are more varied (launch 3 missiles, increase att/def according to how much money you have, deal some damage to all enemy units and lower their fuel to half and so on). If you want a colorful over the top strategy game, pick DS, if you want something more subdued and balanced, pick DoR.
Oh, right, DS has
a war room, which brings a lot of replay value, while DoR has online play, but I've never used it so I can't comment on how it works. If I'm not mistaken you have to finish a match in one go, no saving and resuming
edit: Right, I had forgotten DS's story is connected to the previous games. Even then, from what I remember knowing the plot of the previous games wasn't critical to understand what's going on. I'd say look for a summary in warswiki if you really want to know. Characters pages have their bios separated by game, handy to read as you go or before jumping in