The title kind of says it all- is it better to download the game through Steam or through Origin? CD/DVD purchases are sadly no longer a realistic option, much as I'd prefer to have a physical copy, so this is my first real look at buying a fully digital copy of ANY game. I have no intention of buying everything right off the bat, but given my experiences with TS1 and TS2 I think it's safe to assume that if I like TS3 on a similar level, I'll eventually want to have the option to expand to everything out there.

Looking at the history of pricing on both sites it looks to be roughly even (at least when considering the variability of sales), so that's not enough to sway me one way or the other... Origin is cheaper right now, but not by much and I expect not for long.

From internet research it also sounds like the content available on both platforms is identical- all EPs and SPs are available on both systems, with the exception on each of Katy Perry's Sweet Treats (such a tragic loss THAT will be ) and from what I can gather, the additional worlds from the Store are only available for purchase through Origin, but are actually just a Store download that works on either platform (please correct me if I'm wrong).

The big difference I think I see, and that makes Steam the leading contender at the moment, is that it sounds like the DRM through Origin is/has the potential to be much more intrusive and game-breaking than it does through Steam (if DRM is even a factor there... I can't honestly tell). Assuming I'm reading this correctly, that alone would probably be enough to make Steam the winner, but again, please correct me if I'm wrong. My technical know-how isn't so good that I trust I'm reading everything correctly in my research!

You don't have to sell me on the game itself, just on whether I'll be happier in the long run going with Steam or Origin for downloading it!

I play through Origin and, although it is sometimes a resource hog and a freezy mess, the game itself runs fine and I don't have any game-breaking issues.

Now, since you are just starting off and don't have The Sims 3 on any platform, I recommend Steam. Owning The Sims 3 on Steam will also give you access to the Origin version; via EA Customer Support for base game and Pets (you might have to bug them a couple of times until they realize what you're talking about), and by entering the code Steam gives you for other packs.
At least in Europe, Steam packs are cheaper (€20 everything vs €40 EP/€20 SP on Origin), and Steam has good sales too. An especially tempting sale is The Sims 3 Collection, which sometimes goes on sale for around €60 and includes every EP and SP currently available.

The only drawback I can think of is the lack of the Store content patch (which Launcher doesn't download anymore, but Origin includes it by default), although you can probably find the file online if you really need it.

If you have Origin access from Steam, shouldn't that enable you to download from the store even if you don't play through Origin?

Steam's is DRM-free. That means you can run the game without having to go through Steam. You just need to launch it once from Steam so it create the registry keys, and afterwards you can skip the Launcher and use the TS3W executable to launch the game.

Origin's has DRM that cannot be bypassed. It's also been reported to slow down performance by 5-15% as the game checks you still have Origin running in the background. You can't skip the Launcher either, so it makes the whole process very tedious, as you have to log into Origin (maybe update it), open the Launcher, and then you can launch the game.

Steam it is!