Yep, you can transfer your Sims 3 user files such as your saved games, mods, Sims etc.
Easiest way to copy or transfer Sims 3 game files, (like saved games, mods, screenshots, etc.) is to save the whole Sims 3 folder to a usb thumb drive. - This way everything is saved and backed up. Plus it's easier to copy the whole folder at once.
How to Copy -
Right-click on the Sims 3 folder, select Copy and paste it to your USB drive, take it over to your new computer and copy/paste into C:\Users\Username\Documents\Electronic Arts. It may ask to override your current Sims 3 folder. Say yes, specially if it's a new install.
If you're not comfortable with that or you've been using that folder. You can rename it Sims3old or something like that so you are sure not to loose either Sims 3 folders.
More information in the post linked in the thread below.
[Info.] Transfer Sims 3 Game Saves or Sims 3 Folder to Another Computer
https://www.carls-sims-4-guide.com/forum/index.php?topic=31911.msg507829#msg507829I can't promise that you won't have to reinstall your .Sims3Pack files, due to how fussy the Sims 3 launcher is, but your custom content that is in your mods/package folder should be fine.
If having issues with Sims3Pack files or custom content installing or showing in game, see the post linked below for tips to fix that.
Sims 3 - How-To: Fix Problems with Mods/CC
https://www.carls-sims-4-guide.com/forum/index.php?topic=31759.msg506010#msg506010