Panasonic's AVCHD video format: questions about quality, compatability, conversion
The AVCHD vs. MP4 is just a choice of a container format. When all other parameters are the same, choosing AVCHD or MP4 depends on the use you intend to give to the movie clips that you record. If you plan on doing editing, then MP4 is better because it has the index tables that video editors need to find frames fast using random access. If on the other side you plan to just streaming these clips over to a TV or computer then AVCHD is best as it is a transport stream, so players will have to do less work to play the clip from start to end.

Note that a utility like ffmpeg can easily convert between AVCHD and MP4 without any loss of quality, so really the choice you make isn't irreversible.

What determines image quality is the picture size and the recording bitrate, not the container format. I went to the site that has the specs for your camera and found it offers the following recording options:


[HD Video]

1920 x 1080 pixels, 50i (FSH: 17Mbps / AVCHD) (Sensor output is 25p)
1280 x 720 pixels, 50p (SH: 17Mbps / AVCHD) (Sensor output is 25p) 
1920 x 1080 pixels, 25 fps (FHD: 20Mbps / MP4)
1280 x 720 pixels, 25 fps (HD: 10Mbps / MP4) 

[STD Video]

640 x 480 pixels, 25 fps (VGA: 4Mbps / MP4)



So for best quality you should pick the largest picture size at the largest bitrate. Looking at the above list the best choice is the FHD format, which is 1920x1080 at 20Mbps, and that option is only available in MP4.

The second and third options are at 17Mbps. At that level you have two options, 1920x1080 and 1280x720, both recorded in AVCHD.

Note that I'm not including frame rate in my decisions, since it appears the sensor in this camera can only record 25p.