Elgato Game Capture HD60 is the best you can get right now. 1080p, 60 FPS, and is also capable of streaming.
Downsides is that the software that the device uses is the only software you can use with it, and you also need to be aware of the system requirements for said software. It is only capable of HDMI output, so this is a capture card made for the current generation of consoles.
It is also a pretty pricey capture card, checkling in at over $200. (Last time I checked Amazon, it was on sale for about $180, but it isn't anymore. =P)
Next in line is the Elgato Game Capture HD, which is similar to the HD60, but is only capable of 1080i, 30 FPS. Like the HD60, Elgato capture cards can only use their own software. However, this one can use A/V and HDMI inputs. Can be used for current gen consoles, but is best used for last Gen stuff. Not only that, the system requirements for the software are less beefy.
This capure device checks in at $138 on Amazon right now. (Normally $180.)
Finally, there is the Avermedia C875 LGP HD Game Capture. This device boasts the ability record things without a computer, allowing you to record stuff on the go, but you will need to use an SD card to save stuff in this mode. Also, when in PC-Free mode, you have no control over what your settings are when you record, so that is the biggest downside of the mode. (It records in 720p in this mode.) If you want to control your settings, then use the device with your computer.
This device is currently $159 on Amazon right now.
In my experience, these are arguably some of the best capure devices out there that gives you good quality, as well as ease of use. All of the devices can be used for streaming as well as regular capture.