Handbrake forces you to re-encode the video even when it's not necessary. Not the best choice by any means.
Whenever I have tried to skirt around re-encoding and just alter the container type I have got less than perfect results.
The files play fine, but weird things don't work, like fast forward or re-wind.
The quality loss running it through handbrake is minimal (you'll probably never notice) and it will be full Apple TV compliant.