Terminal Services Web-Access (aka Remote Desktop Web Connection) uses an ActiveX control and only works in IE, and there isn't much point in that since if you have IE then you're going to have mstsc.exe installed too.
VNC is better in this regard because there are loads of Java applet clients for that which are inherently more cross-platform than ActiveX.
RDP is so much more better and advanced... and faster and 1000 other things that I'm afraid VNC doesn't come close to it. I would NEVER work via a VNC client but working with RDP is a pleasure.
But yeah, that web thingy won't run on these "thin" clients so :/