Wondering what the comparative might be between these two formats in terms of quality.
MPEG4 is the codec standard - AVCHD and H.264 are two different variants of MPEG4. What you need to be comparing is MPEG2 and MPEG4.
Both can be made to look equally good, if time and hard disk space were not a concern. MPEG4 was developed for a more efficient compression in terms of space - so if hard disk space is a concern this is preferred. HDCAM SR is MPEG4 based.
So, broadcast HD quality at 20 to 25 mbps in MPEG2 is about the same as h.264 at around 12 mbps.
Broadcast quality according to big networks is a minimum of 50Mbps interframe at 8-bit 4:2:2 chroma subsampling from a 1/5" 3CCD Sensor (12.7mm) - and both MPEG2 and MPEG4 are interframe codecs. Whatever you shoot, you'll still need 50 Mbps to pass muster. 1/3" 3CCD cameras and lower are not accepted. There are always exceptions, of course.
The GH2 unhacked is not a broadcast quality camera. Until August 30th or so, the cheapest camera that records directly to a broadcast quality codec (without using an external recorder) is the Canon C300. After that date, it might be the Blackmagic Cinema Camera. I say 'might' because the BMCC has a small sensor and it will probably be tested specifically, but I don't see any reason why it should fail.
Another cheap option is the Nikon D800 with a Ninja 2.
AVCHD is not the same as H.264 - think of them as twins who look the same but are not - both daughters of MPEG4. However, for all practical purposes, they have the same 'sort' of characteristics and issues.
Your choice of codec would depend on your workflow and specific delivery requirements.