Echoing what the others have already said, the intro and outro could use some work, but I really enjoyed the track, and you've got that middle section absolutely nailed. Pretty good recording for a band practice too!
Good tight playing for the majority, which is always pleasing on the ears.
I think it works just fine without the keyboards!
Personally I'd try making things a little heavier with some nasty deep guitar grunty-riffs (fairly low output) under the vocal sections, and maybe just after that too. I know it's a cover, of course, but you're making it your own and that's great.
BTW I didn't particularly like the original so you've done a cracking job here ;)
Roo