You actually have many

You actually have many options available here and will likely have more trouble deciding which is best solution that works. Personally, I always use AppGeeker video converter, it can minimize the loss of video quality, and you can tweak the output setting for a specific need. At least, i am satify with its output result.

Here is the guide on MTS to AVI available: http://www.appgeeker.com/how-to/convert-mts-to-avi-mac.html