Sure, but try this first. On your S4, goto Settings > Applications (or Manage Applications). Select All Tab in the top next to Running, Downloaded etc. Select WhatsApp application in there, then tap Clear Data. Tap Clear Cache and then Uninstall it.
Now, on your S3, open WhatsApps, Menu, select Settings, select Chat settings and select [Backup conversations].
Then connect the the S3 to your PC, open My Computer > Phone > sdcard folder. You can find the WhatsApp folder in there. Copy that WhatsApp folder from there and paste it to your PC. Now you have the backup of your WhatsApp folder from your S3.
Now, connect your S4 to your PC, open My Computer > phone (i9500) > sdcard folder and then copy the WhatsApp folder to there from your PC.
Make sure you take out the SD card before doing these steps. Then install WhatsApp on your S4. Did that work ?