Do you get more mileage while using a IGH vs. Derailleur?
Yes! Surely! The primary reasons are twofold:
1) The chain does not have to bend sideways to accommodate a range of gears. This is true at both ends -- single chainring, single sprocket/cog. The chain incurs less wear by running in a straight line.
2) There are (for Rohloff installations using eccentric bottom brackets or sliding or ramped dropouts) no small tension pulleys for the chain to wrap around. This removes a major wear and friction point. Of course, for Rohloff installations using a derailleur-like chain tensioner, there is no difference in this regard.
Because the chain just runs in a straight line without lateral flexing, it does wear much longer than in a derailleur application. Also because the chain does not need to move laterally, it is possible to fit a "floating" chain case (i.e. Hebie Chainglider) to fully enclose the chain and protect it from grit and water exposure and lubrication loss. Of course, this will only work with some chainring/sprocket combinations because Hebie only makes the Chainglider to fit specific applications.
Best,
Dan.