All I wanna know is, "Can I develop high quality games for Android/iOS using libGDX or game engines like Unity3D would be needed?"
Unity3D is much more than a library (like libGDX). You get a very good editor, that allows you to see your game objects and make debugging a dream compared to building something without a visual aid.
Unity3D has another major advantage in its asset store. Whenever I want to do something new, I look into the asset store first, and usually someone else has done it, with much better quality than what I'd achieve in a small time frame.
I did this game in Unity3D: http://www.youtube.com/watch?v=x6-5D6IkD5E and while I could have done it in many other engines, it would have taken me much longer.