I agree with what @MoritzLost said. Better that you copy those video files directly.
Once you have these MTS files copied, there are a variety of options. I ran into this problem myself recently and found the two best options were rather simple (despite lots of complicated discussions online):
Simply rename (or copy first and rename the copy) the video file from a .MTS extension to .MP4 extension.
Sounds a bit stupid, but the video and audio are generally supported by lots of different programs. Problem is, the MTS container surrounding the video and audio streams us bit as well supported. Give this a try first, because it's the easiest thing to do with keeping the audio and video quality exactly as it is in the original file.
The next best option I found was using ffmbc. You can find the website for it (which will eventually be unsupported or removed completely) at: https://code.google.com/p/ffmbc/ . There is also a Google Groups website for it at: https://groups.google.com/forum/#!forum/ffmbc-discuss . For the Windows version, you'll find a download on the Groups website, while for Mac and Unix/Linux, you can download and build the code yourself (sorry, I can't help you with building on a Mac).
After you have the program built, you can run the following command:
ffmbc -fflags +genpts -i "FILENAME.MTS" -vcodec copy -acodec copy "FILENAME.mp4"
Obviously, you'll need to make sure ffmbc is runable from the command line of whichever OS you are using...otherwise, you can use the full path to the ffmbc executable. And change "FILENAME" to be the name of whatever file you are using.
**From my experience, you will find the resulting file to be smaller. For some reason, the MP4 container format is more efficient than the MTS container format. You could research the reasons behind this, if you're interested. Anyway, I have found that with a 6.1 GB file, repackaging an MTS file drops to about 5.7 GB. The time it took to repackage that particular file from MTS to MP4 was about 1m 30sec. So, even if you have incredibly large files, you are not looking as nearly the length of time that you would for re-encoding the video/audio.
You could also try using ffmpeg, MP4Box, Libav, are a variety of other tools. The key here is that you do not need to re-encode the audio or video (unless you want/choose to). You simply want to change the container that "holds" the video and audio streams.
**Generally speaking, the AAC audio format is better supported and standard for MP4. So, you might want to copy the video stream but re-encode the audio if the application or media player you're using doesn't support AC3 (the default MTS audio format). Re-encoding the audio won't take much extra time, but will add time compared to simply repackaging the video/audio in a different container.
Also, if you need to change anything, such as framerate, resolution, audio bitrate, etc., then you'll need to re-encode the audio or video (or both). But, if you literally want the audio/video to be the same, the container change is your best choice and the fastest (with the exception of if renaming the extension MP4, if this works for your purposes).
