The video posted above gives a more indepth review of these devices.
I've been putting up YouTube videos since early 2009. Back when I first considered posting YouTube videos, I remember having no idea how I would capture my video game footage. I began with a cheap KWorld capture device that was very similar to the $10 EasyCap. It was a great starting capture device and allowed me to capture retro consoles for a cheap price.
Eventually, I decided to upgrade my equipment to capture HD gameplay. I chose the Hauppauge HD PVR Gaming Edition. When I received it in the mail, I was severly disappointed when I realized that it could not capture any footage prior to Xbox 360, PS3, and Nintendo Wii. This meant I couldn't capture any footage for the games I wanted to review from console like Super Nintendo, Sega Genesis, and even Playstation 2.
I finally upgraded to the Elgato Game Capture HD. It is a major improvement over the Hauppauge HD PVR in so many ways. The first is it's size. The Hauppauge is actually approximately the same size as a Nintendo Wii U itself. The Elgato is the size large cell phone. What's more important is that the Elgato allows footage to be captured from any console - Retro and Modern. It captures crystal clear 1080p footage and uses HDMI.
If you are looking to start posting YouTube gaming videos or even just want to capture gameplay footage for your own personal use, I would highly recommend buying the Elgato Game Capture HD.
System Requirements for Elgato Game Capture HD:
Mac: OS X 10.7 or later, 2.0 GHz Intel Core 2 Duo CPU
PC: Windows 7 or later, 2.0 GHz dual core CPU, sound card
4 GB RAM, built-in USB 2.0 port