This is a mostly stream-of-conciousness account of converting a couple MTS files to a much more useful format and container. I did this on Arch Linux, but it would be nice to have something for Windows users too.
for i in *.MTS; do ffmpeg -i "$i" -c:v copy -c:a aac -aq 0 "$i.mp4"; done
But, as it turns out, Sony splits the files at 2GB, defeating the entire purpose of using exFAT in the first place (overcoming the 2GB filesize limit of FAT). Come on, Sony. Apparently it's possible to concatenate the files losslessly, though it's a small hassle. I would rewrite this as a script with temporary files (or fifos where supported) if I would be doing this a lot. If you have long videos, you better have plenty of disk space to spend on temporary files.
This is where the code starts to get a little filename-dependant. In a script, this would be more clever.
ffmpeg -i 00120.MTS.mp4 -c copy -bsf:v h264_mp4toannexb -f mpegts intermediate1.ts ffmpeg -i 00121.MTS.mp4 -c copy -bsf:v h264_mp4toannexb -f mpegts intermediate2.ts ffmpeg -i "concat:intermediate1.ts|intermediate2.ts" -c copy -bsf:a aac_adtstoasc output.mp4
And it works! You end up with an h264 video, aac audio, and an mp4 container.
As for a Windows solution...
This seems like good project for python practice. A python script ought to work in Windows, if you've got the right pieces.