If you download your games from origin onto another computer, your saved games will be lost unless you back it up. Here is what you do:
1.) Go to My Documents>Electronic Arts>The Sims 3
2.) Get a USB flash drive
3.) Copy the "Saves" folder and paste it into your flash drive.
4.) If you have mods or custom contents, make sure to copy and paste those too.
-If you have mods, copy your "Mods" folder and paste it to your flash drive.
-If you have custom contents, go to My Documents>Electronic Arts>The Sims 3
and copy the DCCache folder. Paste it to your flash drive.
5.) Safely eject your USB flash drive.
6.) Download all games from origin onto the other computer.
7.) Run your game once and quit when you get to the screen where you choose your game. (This is to let the game make the required folders in My Documents.)
8.) Go to My Documents>Electronic Arts>The Sims 3
9.) Plug in your USB flash drive.
10.) Copy everything in the backed up "Saves" folder (from your USB) and paste it into the new "Saves" folder (on your new computer).
11.) If you have mods, copy the backed up "Mods" folder (on your USB) and paste it to My Documents>Electronic Arts>The Sims 3 (on your new computer).
12.) If you have custom contents, copy everything in the backed up "DCCache" folder (on your USB) and paste it into the new "DCCache" folder (on your new computer).
13.) Close out of everything and run your game. On the screen where you choose your games, you should see the games that were previously on your old computer.
Note: If you choose not to backup Mods or Custom Contents, the items will be replaced with game items. It's not a big deal, so don't worry about it.
That took a long time to type .___.
I hope it helped you! (: