We highly recommend the first two: Aiseesoft Total Video Converter, Aiseesoft Video Converter for Mac and Tipard Video Converter. They are both all-in-one software which could satisfy all your needs in multimedia world with great features and quality.
With this professional TS Converter, you can play your TS files on the mainstream video players like PSP, iPod, iPhone, Archos, iRiver, Zune, Creative Zen, Apple TV, Blackberry, etc.
The mts file format is extension of AVCHD video format which is based on the popular MPEG-4 video codec. It is developed jointly by Sony and Panasonic. The format is used by a number of digital camcorders like Sony, Panasonic, and Canon.
Actually, MP4 file is multimedia file, which is a container format that can store video, audio and subtitle data. MP4 format is really popular because many stores like iTunes are using this container format, iPod and Playstation Portable (PSP) and other popular devices support MP4 format.