The Easycap Capture adapter is simply a video capture device with no TV tuner, so you would not be able to receive any TV signal.
I would recommend the USB TV tuner. I'm not sure whether you will need an Analog or Digital tuner as this will vary according to where you live (here in the U.S. all stations are now Digital). If you are putting this into a desktop computer you can get an internal TV Tuner card. Hauppage makes a few good ones that will work with Windows, both internal and USB. Their products also come with software to allow you to watch and record TV. They should also work with other programs.
As for performance the TV Tuner and the Video capture card should be about the same. The TV tuner is in hardware and the video capture for both is also in hardware. If you are concerned about performance, your best bet is to get a device that has a hardware MPEG-2 encoder (usually an internal card). With my Hauppage card with built in encoding, I was able to watch TV and record without any serious performance hit to anything else I was doing at the time.