Yu Televentures is a subsidiary of Micromax. In fact, the CEO of the both the firms remain same.
Technically, Micromax seems to have no say in what is being handled by Yu. Yu has a better set of hardware and after sales service. Yu Televentures is a joint venture between Micromax Corporation and Cyanogen Inc.
It would be a good decision to buy a Yu branded smartphone. They excel in warranty issues and believed to offer excellent after sales service. Yu has recently started the unique Door-To-Door support.
Yu is the Brand which has been founded in 2014 December and this Brand is jointly held by Micromax and Cyanogen.
Yu also holds the right for Cyanogen Os in India, so it is a good brand to Buy.
When you're looking to buy a mobile, don't just follow the specifications, also look on to what Chipset they are using and also the detail specifications, which you can get in GSMarena ( which I follow regularly).