If you want to use Origin version of anything on your game, or use Origin to download your updates. It is usually best to just switch to Online DRM. The Origin Online DRM has actually become quite a lot better in recent years, especially after the famous Sim City fiasco forced them to overhaul their entire system.
To do this, just register your Sims 3 games with your EA/Origin account, then download the game.
This is also the procedure if you want to switch from Steam to Origin (unfortunately you can't do the reverse.)
NoCD Issues Note if you are using the Origin updater
As a note, if you a running a game installed from disk and expansions installed from Origin or the other way around, this creates an unusual. The game seems to try to use both DRM methods. (Thanks EA! *sarcastic*) This breaks NoCD.
I recommend either sticking to disks and the superpatcher or going with Origin to install your entire Sims 3 library (unless you use Steam, in which case you might want to get your expansion pack library from Steam.)
I recommend either sticking to disks and the superpatcher or going with Origin to install your entire Sims 3 library (unless you use Steam, in which case you might want to get your expansion pack library from Steam.)