How are you using TV -- are you connecting local? How are you using RDP - local? As sc302 mentions there is a huge difference between doing these technologies on the local lan vs interent. Don't you have a 150mbps connection, what is your upload speed?
Where are are you at and what is that speed for internet?
I use both TV from work and RDP through a openvpn connection to my home network. Both work just fine - I normally just rdp in because I normally have the vpn connection open. But if something goes wrong with the vpn I TV in, etc. I will do some testing to see which one works better today from some sort of fps? How are you measuring this? I don't recall RDP showing any sort of FPS number? But maybe I never looked.
Also if you want to use rdp from remote, you also need to know what your public IP is or us some form of dynamic dns to get your public IP.