When Ben gave the walkie to Miles I initially thought it was for connecting it allowing Miles to know what was happening at Dharma Ville with Smokey. I don't know if it was connected, but I think I know why Ben killed Widmore. Widmore didn't want Ben to hear the critical information of what was his purpose on the island involving Desmond as was revealed to him by Jacob. When Ben realized he was not going to hear the information he killed Widmore to obtain exactly how Desmond is going to do that from Widmore's body through Miles powers. Apart from revenge, I think Ben, the master of manipulation is preparing his last double agent game.