I would buy Mass Effect 3 DRM-free through GOG.com, like Witcher II and PlaneScape: Torment. I would buy it with Steam DRM. Every single experience I have ever had with EA Origin has been horrible.
I recently bought Dragon Age and Dragon Age 2. I had to download each multiple times because EA distributed faulty keys, could not provide notice when a correct key would be provided, and required the complete re-download of the entire 12 and 8 GiB games just to get a new key. It took approximately 10 days of continuous re-downloads until the installer worked. Then, the launcher refused to allow me to start the game until I made an EA Origin account. So I made an EA Origin account, which took another day because EA's servers kept returning errors whenever I tried to make an account. So, I try again, log in to my EA Origin account through the Dragon Age launcher. Then Dragon Age launches and I have to log into EA Origin again. ... Okay. At this point, I'm prompted for my product keys again. Yes, the same damned keys I got from EA Origin and the same damned keys I already entered during installation. Okay. Now, my game came with DLC. No... it didn't. So I spend the next four hours hunting down the DLC I paid for. I have to download EACH AND EVERY DLC INDIVIDUALLY and run their separate installers which each seem to have some automatic delay built in. One of the things I have to download are the PC high resolution textures, for the PC version of the game I downloaded. I would not have even known about the low quality textures if I hadn't had the foresight to check that my DLC was already installed.
Basically, EA is a really incompetent publisher. Origin is an incompetent effort. Even if it worked, it would still have all the other problems people have mentioned. Maybe EA is really good on the developer side, or maybe their heavy-handed crap works well in the console market, because the console platform developers can hit them back.
Do you know what doesn't suck? GOG.com. Know what else doesn't suck? Steam. Two clicks to buy a game. DLC automatically installs. You only have to deal with CD keys if the game developer or publisher decides to keep their CD key authentication system when they sell on Steam. If you have to enter a key, Steam gives it to you on the Steam console when you start the game up so you can copy and paste it into your game.
You can really tell the difference in focus between Steam and Origin. Steam is focused on customers, like Amazon.com. They have exceptional customer service, and focus on making things as simple and stream-lined as possible for the customer. EA Origin is focused on Steam, and trying to push Steam out of turf they want to take a profit out of. EA cares about "market" in MBA-retardese. The concept of the "customer" can take a flying **** as far as they're concerned.