USB will be faster. Keithley also says this in one of their docs (1KW-61357-0_DMM6500_Datalogging_Application_Note_080318). The LAN interface is 100BT only, the USB 2.0 interface can go up to 480Mbps.
Also see github.com:tektronix/keithley, in instrument examples/DMM6500/Streaming...