A structured training plan with tough days hard enough to force adaptations and rest days/weeks/month easy enough to leave you fresh enough to go hard increases your power output. When that yields a good power to weight ratio you're fast up-hill. With good power to drag you're fast on flat ground. Doing it on flat ground or in the hills doesn't make a big difference.
Having lived in the Colorado Rockies but done more riding on the east side of Boulder I'd argue there's no practical difference until you run out of gears. Equipment choice can usually avoid that and you could always spend some time at low cadence on flat ground with your big ring if you noticed unacceptable power output issues at low cadences.
I like the _Training and Racing with a Power Meter_ anecdote about the racer who blew up and got dropped every time he spent more than five minutes at his one hour power but a cadence of 70 or below. He got lower gears.
Psychologically hills are different. For better (you need to ride hard enough to force training adaptations) or worse (you're not going to ride at intensity long enough if you over do it) many people find it easier to push themselves up-hill.
Last edited by Drew Eckhardt; 05-30-13 at 10:25 AM.