Could it be just your carrier version? I know some US carriers put their own dialers and contacts, which look hideous.
I'm not sure what gestures are you referring to. The left to text, right to call?
If so, then I do have those, on my LTE 32 International Unlocked.
By the way, if you like the Android stock dialer, why not opt for the Google Play version S4? I personally don't like the vanilla. It has half the features of TouchWiz.
You could try google for Nexus dialer/contacts apk. But keep in mind, you might not be able to flash it, given it's an android 4.3 based. Unless you look for an older apk, 4.2 and earlier.