Ku is not up to the task, but works globally. The Ku planes get to share a ~8Mbps beam, which is why there are so many complaints about the 747's/777's being slow.
There are plenty of complaints about slow internet on the Ka equipped aircraft as well.
The fastest airborne download speeds I've seen have been on the Ka system. But I've also had very respectable (18 mbs) speeds on the Ku band aircraft.
And note that the Ku is not installed just on the 747/772, but the entire widebody (and 752 international) fleet, as well as the 319/320s.
IME the Ku system is more than adequate for everything except video streaming. The biggest issue with both Ka and Ku is latency, which makes using apps such as Citrix extremely frustrating.