When using the same type of install as before (i.e. disc, or Origin, or Steam), you can transfer the installed store files to your new game folder, no need to redownload anything. Here's what you'll need to copy over:
- Every file in DCCache that ends in .ebc (the files ending in .dbc are bundled third-party custom content)
- Only ccmerged.package from DCBackup; the others are duplicates of installed Sims3Packs (store and cc) and can be trashed
- The files from InstalledWorlds
Here's a full list of everything in your game folder, in case you want to keep anything else:
https://sims3.crinrict.com/en/2011/01/faq-user-files.html
If you're coming from a Steam install, you'll definitely need to reinstall your store stuff, as the Origin install won't recognize the content. It's usually fine to transfer from a disc to an Origin install, but occasionally it doesn't work. In any case, just test in an otherwise clean folder and make sure all your store stuff works. If not, you could try copying the Sims3Packs from Downloads, but if that didn't work either, you'd be stuck downloading everything fresh.