(I don't know if I'm allowed to reply to a thread titled "no reply"...)

I listened to both versions and I like your voice better.
First, I don't think Asterian's voice fits this song, and second, I don't think your voice is bad.

Could your vocals be improved with better post production?
I think so.
But the rasping is NOT your problem, it gives your voice a unique quality that I wouldn't process away.