sadly with RDP you cannot have same experience.it is not about 1 or 2 site , for example for me , my vpn connection is always on because there is not internet without it.but with RDP loging into another machine , with all lag you see , is almost impossible at least for power user like me which most of the time have 50+ tab open in chrome in site's like youtube , android dev doc's, etc.
But you have to send a packet every time the remote screen changes. It is much more demanding on network resources than a VPN and thus will be more difficult to use on a daily basis.
Why nos havig a local cache like wwwoffle (someone has to reimplement such a thing) or squid? that way you won't need a connection just to browse a bunch of (mostly static?) html pages... just sayin'.
