Question

I need to connect mixer via headphones output. Is the sound quality/volume the same as from main output?

Answer 1

You can see the specs on the headphone amp and the line outputs here:

http://www.presonus.com/products/AudioBox-USB/techspecs

If you're using a different kind of AudioBox you can check the tech specs on the device's respective product page.

The configuration you're describing may serve your purposes just fine but it is not recommended or supported.