Note: This will install over the current S-Voice app and the .apk file works on both my Galaxy S3 and Nexus 4.
Step 1: Enable Outside Applications
Go to Settings -> Security and make sure to check "Unknown Sources"
Download the S4 version of S-Voice app right here. You can download this directly to your GS3 or transfer it from your computer. From there, install as you would any other app.
You may find it's hard to know what's different here. There is a new weather widget (nice!), and a bunch of new tasks.