After analyzing many comments to part 1 of the video comparison, it's time for an IMPORTANT UPDATE regarding resolution and moiré issues!
Most of the comments critisized the stronger tendency to moiré of the NEX-7. On the other hand, many viewers remarked, the GH2 settings produced too much contrast, so that the GH2 video looked sharper but lost details in dark areas (shadows etc.). Some readers suggested to try different film modes on the NEX-7 as well as on the GH2 and to compare also to a hacked 720p50 mode. So I made another test with the NEX-7 set to "landscape" and to "vivid" film modes. The GH2 was set to "smooth".
Another issue commented by many viewers was the remarkable difference in detail resolution. After a more detailed analysis of the source MTS files and the rendered output from Adobe Premiere Pro (CS5), I recognized a severe misinterpretatation of the 1080p25 files by Premiere Pro. The software interprets those files as interlaced footage and renders only half of the vertical resolution to the output file resulting e.g. in stronger aliasing and moiré. This happened only to the 1080p25 files (from NEX-7 as well as from GH2) but not to the 1080p50 or 1080p24 files. In order to avoid this when you create your own content, you will have to change the interpretation settings of the source files manually to "progressive" in Adobe Premiere Pro!
This second video already takes into account that problem and the resolution of the rendered output (of the uploaded file) is now adequate to the original footage. The first part is still rendering and will be replaced soon as well. There will be a comment on the first part when it was updated, so please check back for that later.
Regarding the content of the second part:
There were two cameras used, again the NEX-7 with Voigtlander Nokton ASPH 35mm/F1.2 (adapted with a Novoflex adapter) and one hacked Panasonic Lumix GH2 with Leica DG 25mm/F1.4 ASPH. There are two sequences in which the NEX-7 is compared to the GH2 mounted side-by-side on a tripod. The cameras were set to default contrast and sharpness but to different film modes at base ISO (160 for the GH2, 100 for the NEX-7), white balance was set to AWB.
In the first sequence the 720p50 mode of the hacked GH2 (V1.0 with 36 Mbps) is compared to the 1080p50 mode (28 Mbps) of the NEX-7. The section of the GH2 video was subsequently upscaled up to 1080 lines. The shutter speed was set to 1/100s. The aperture was set at F5.0 on the GH2 and to about F4.0 at the NEX (due to its lower ISO sensitivity). The NEX-7 was set to film mode "landscape", the GH2 to "smooth".
In the second sequence the 1080p25 mode of the NEX-7 at 24 Mbps is compared to the 1080p24 cinema mode of the GH2 patched to 32 Mbps. The shutter was set to 1/50s, aperture F7.1 at the GH2 and appxoximately F5.6 at the NEX-7. The NEX-7 was set to film mode "vivid", the GH2 to film mode "smooth". The interpretation of the 24p video was changed in Premiere Pro to 25 fps to avoid artifical frame inserts, as a result you see it sped up by 4%.
The NEX-7 still produces remarkable more moiré as the GH2, the film modes "landscape" and "vivid" seem to have not influence on that. But as the GH2 video with film mode "smooth" looks less crispy and contrasty now (but preserves the shadows better), the NEX-7 videos gain some contrast and visible sharpness. In combination with the corrected interpretation of the 1080p25 footage, the 25 fps videos look much better now and the NEX-7 video quality comes closer to that of the GH2.
The Vimeo video that you find embedded here is NOT applicable to judge the quality of the ouput of these cameras due to the fact that the original FullHD 1080p video was rendered with 32 Mbps to 25 frames per second (fps) and the video that Vimeo streams is re-rendered by Vimeo at about 4.5 Mbps. As a result, you will see a video with less details and a lot more artifacts. So, to get a realistic impression, you will have to download the master file that was originally rendered and uploaded to Vimeo. If you are a registered Vimeo user, you find a download link on the Vimeo video page (please right click that link and select "Save to..." in order to download that file). This resolution and this high frame rate requires very powerful ressources from your playback equipment. Only systems that support hardware H.264 decoding on their graphics card will be able to play it without judder. The MediaPlayer included in Windows 7 supports many hardware accelerations of today's graphic cards, so chances are good with that player. VLC's support for H.264 hardware decoding are still experimental and must be explicitely activated in the VLC player's settings. If you have very powerful ressources you may try the 1080p 50 fps version as well, that you find here: http://vimeo.com/36224110 (but please also download the source file, as the Vimeo rendering to 30 fps is awfully choppy with a lot of judder). For the sequences that were recorded initially in 25fps, the 25 fps version is fairly enough, only the 50 fps sequences loose some information accordingly.