That's where it gets tricky, he basically doesn't have any special powers, besides those that angels have, Which to be honest, I have no clue what they are.. flying? materialization? sounds more like sci-fi than religion. I would have to do some research as to what exactly angels supposedly have as far as power, but I don't think any supernatural ability gives you the automatic "God" title.
I think Lucifer exists, to try and persuade mankind to renounce God, it's sort of like every hero in every story ever told needs an anti-hero, a villain. Lucifer is God's anti-hero.