The lag time is highly bandwidth dependent with Hamachi. I have business-class cable internet (40 down, 5 up) at both my home & office, and the responsiveness is very usable.
Even with upload speeds of 5 MBPS, I would still opt for Remote Desktop. You are pretty limited in transfer rates. 5 MegaBITS/second is about 0.625 MegaBYTES/second where as your standard USB flash drive copies data at about a rate of 15 MegaBYTES/second. Having operations carried out at the host computer would be a lot better, which is why I recommend RDP and LogMeIn. Hard Drives read rates are around 60-80 MegaBytes/sec With RDP and LogMeIn, it's basically streaming your screen.