This is a guide to controlling your TV using Google Home with the Logitech Harmony Hub and IFTTT. There is also a brief overview for controlling your TV with the Google Chromecast. The best way to control your TV with the Google Home is with the Harmony Hub. In order to configure this, you must use the IFTTT app, which allows Google Home to communicate with the Harmony Hub. Another alternative is using a SmartThings Hub to allow the two hubs to communicate. 
Unfortunately, control is limited to starting/stopping an activity. You are not able to control volume or directly tune to favorite channels like you can with the Amazon Echo.

This is a brief tutorial for controlling your TV, stereo, and other devices using your voice with the Amazon Echo. This requires an Amazon Echo or New Echo Dot, and a Logitech Harmony Hub. This video has a step by step guide for integrating these devices for voice control. It also explains how to allow Alexa to control more than one Harmony Hub.

The Alexa app has recently been updated with a new Harmony skill that allows volume and pause/ff/rwd voice controls. It's a little tricky to use but not too difficult once you understand how it works but this overview will help.