What is the widest range IGH available? (and how does it compare to derailleurs)
The Rohloff "500/14 Speedplay" has 14 gears and a difference of 526%, so the fast/high/hard gear is 5.26 larger than the slow/low/easy gear.



So this is roughly equal to a MTB 24/34/44 triple and a 12-34 rear cassette, which would have a range of gears of 519%  

An advantage of the IGH generally is that the gears are sequential so there's only one action to move through the range.

An advantage of the derailleur bike is that the gears are closer together in broad swathes so you have smaller jumps between gears.

Neither MTB nor Rohloff bike has the high gears of a fast road bike, like a gear of 52front/11rear but there are not a lot of times when such gears are needed outside of racing and fast downhills.

Much more reading at https://www.rohloff.de/en/experience/technology-in-detail/gear-range-comparison/ and https://en.wikipedia.org/wiki/Rohloff_Speedhub