DMed and played. Short answer: almost exactly the same.
By dragonborn campaign. I gave everyone the variant human stats and feat, but they had to earn their resistance and breath through questing (it was part of the story, dragonborn were essentially (d)evolving into humans). So the story was basically, find out why this is happening and either help it along or reverse it.
If you treat a race fairly like real, living creatures then it really is only a light bit of fluff that comes out differently. There is usually a central theme to any society, perhaps for Tieflings it's demons, or dragons for dragonborn, or rocks for dwarves or pranks for gnomes or trees for elves, but those things only provide a basic guidance on how everyone these should play out. There will be people for and against those things. There will be extremes and moderates of both of those groups, there will be people who are indifferent to the subject. There will be issues that are related and likewise, for and against, strongly and not. There will be gods related to those issues. And once you've got all that down, then honestly it doesn't matter what the base race is since the original fluff only provides a general flavor to the campaign.
It was no different than the all-human game I played in, save that we had scales and muzzles and various dragon themes instead of flesh and eyebrows and more humany themes.
I also run a "silly" monster game, that is substantially different, but that's the point. It's monsters!