Is a Roadie with wider tyres still faster then a MTB with slicks?
I'd recommend a Cyclocross bike (also called CX).  That's a robust road bike frame, configured to accept tyres up to about 40mm wide.  You won't need 40mm unless you're doing proper off-roading, but a nice 30-35mm file tread such as a Specialized Trigger or Schwalbe Sammy Slick will run nicely on smooth pavement, will handle cobbles and bad pavement, and will also handle mild gravel/dirt.  

I have a setup like that, and the thing that I love about it is that I can ride pretty much anywhere from road to gravel to bike paths to rail trails to single track (except for MTB trails with lots of rocks!).

Have fun.