This is exactly what I did. I replaced the two 580 II with two 600s and the st-e3-rt.
For me the biggest plusses are:
Easy of use, everything can be driven from the camera (1DX), for example changing to HSS, just do it with the camera menu and the flashes change straight away to HSS. With the 580s you had to change it on the flash as well.
Radio control is a real plus. I use the small lastolite softboxes and was always cursing the line of sight issue, I mean the the soft boxes were "blocking" the optical transmission.
Radio control works fantastic, I put one behind a car and it happily fired.
Another (minor) plus is the extended zoom to 200 mm with 600s.
It was a lot of money to change, but as far as I am concerned, it was worth the money.