Onkyo TX-NR807, front panel flipped down
The TX-NR807 is the most interesting of the two: on top of normal AV receiver functions, it adds streaming audio functionality from Pandora, Rhapsody, Sirius and Internet radio (using vTuner's database of stations). It's also DLNA 1.5-compliant and capable of playing back MP3, WMA, FLAC, Lossless, Ogg Vorbis, and AAC files from network-attached PCs and hard drives.
Onkyo TX-NR807, back panel
Aside from audio streaming, the TX-NR807 has six HDMI inputs, analog video upconversion to 1080p, and onboard decoding for Dolby TrueHD and DTS-HD Master Audio. The TX-NR807 is THX-Select2 Plus certified, which means THX gives it the stamp of approval for rooms where you'll sit 10 feet away from the speakers. Generally, we don't put much stock in THX certification; it costs the manufacturers money without adding performance and there are great sounding receivers that lack certification.
Onkyo TX-NR807, remote
The TX-NR707 is very similar to the TX-NR807, but it lacks the audio streaming and networking features and has less power.