I suppose that it might be possible to have the game installed twice on the same machine, but that's a dodgy way of doing things, so you'll need to remove your Steam game before you can install from Origin. My advice is to use whichever one you like best, but keep in mind that the choice may lock you into a particular vendor for future purchases. So, at some point, every player is probably going to have to choose which client they want to use.

As long as you register your Steam-purchased content with EA (registration steps are in the next section), you can download and play it from Origin, at least as of summer 2014. While Steam content will not install on top of your Origin installation, your Steam product keys will work. In other words, the product key that you get from Origin will not work with Steam and the downloaded content from Origin will not go on top of your Steam installation. You can purchase The Sims 3 (and all of the Stuff Packs and Expansion Packs) from Valve and play them through the Steam client, or you can purchase from Origin (and probably a few other vendors - I haven't really checked), but what you purchase from Origin cannot be installed on Steam. In this instance, Valve and EA are not playing nicely in the sandbox together. Valve, EA, Ubisoft, and the rest are working hard to tie games into their clients and there isn't anything we gamers can do about it other than either not buying their games or learning to live with the problems the vendors create. But kind of like the browser wars of the 90s, the game client wars are in full swing and gamers are caught smack dab in the middle. It really chaps my hide when I cannot fully enjoy a game that I purchased from the vendor where I purchased it.

The short answer to this question is 'sure', depending on whether you like taking advantage of sales from other vendors or not.

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