I have 2 S4. On one the 4g stays grayed when WiFi is running. My other S4 has the 4g on while WiFi is on. In each case, neither shows any 4g activity (arrows moving) with WiFi on. This is rather odd since both are setup the same with regards to WiFi and mobile data.
Update: by turning off Caller Name ID app, I have both of my S4 acting in the same way (4g consistently grayed out when WiFi on). Why the app affects the 4g icon is beyond me.