This leads me to believe the BH is putting out a lot more power than the Bosch, I have never experienced the Bosch lifting the front wheel no matter how steep, but knowing Bosch, they could have measures in place to stop this ? This can also happen if you carry a lot of weight on the rack, battery, panniers etc..
On steep off road stuff, the front end lifts off the ground
The bike certainly eats the battery though, which is the complete opposite of the Bosch motor. Even in turbo mode it seems to just go on and on.
You haven't been the first to mention cadence, and this is something that I'll have to investigate further.
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Also when you say "eating battery" this also leads me to believe it's running a fair bit more power than the Bosch.
On the website it says 350 watts, but it could be putting out a lot more peak power.
Also hubs are not so efficient climbing steep hills as they usually need to spin fast to be more efficient this is where the chain drive works best, when the motor starts to bog down just drop a few gears and off you go, with a hub you can't do this and as it slows and becomes more un-efficient the more the power turns to heat.
I would be careful if climbing a lot of very steep hills with a small hub, keep an eye on the temps, if it's a geared hub and it's hot on the outside then it's roasting on the inside.
A direct drive hub can dissipate heat better.
A conway E-rider Extreme would be a really cool bike to test, I bet it would eat a 23% grade.
But back to cadence, yes you do have to pedal hard and fast for the Bosch to apply full power, this isn't a weakness of the motor but rather a clever way of Bosch making you get some exercise and this is why I like it so much because it matches my cadence brilliantly and I like to put in effort, but I usually only use the motor when I need to. When I'm not in the pedal hard mood then I switch to turbo for short non exercise trips and this is where the DSram DD3 hum really shines.
I would love to try a NuVinci auto hub but I bet it is far from pedal efficient.