The difference is recuperation of EVs.

Do you have a real-world example where it is preferable to use a certain route alternative because of recuperation?

Ideally it would factor in battery charge levels at departure, ideal charging stations along the route, the time to needed to recharge the battery at charging stations along the route and arrive at the destination with enough battery. A custom model may be necessary, but with the world transitioning to EV's it may be worth integrating it into GraphHopper as a profile in the future.

I would do the (de)charging (or recuperation) after calculating the route. Sure, there are algorithms for energy optimal routing, but negative weights might not be that clean to handle in normal Dijkstra (or the speed up algorithms we have). So instead I would tell the algorithm to calculate an "energy optimized" route and avoid uphill, prefer downhill, avoid fast speeds (etc) and then I get one and a few alternative routes with elevation and all the other data back I need for energy calculations. This could be done within GraphHopper but I'm unsure if we should do this as this depends on the driving behaviour, car type, temperature and many more data which is probably better handled on the client side.

Now, the ideal charging stations along the route is a problem which involves yet another step similar to a vehicle routing problem (or travelling salesman) where one could use another tool we developed called jsprit. We have written a blog post a few years ago with the simpler situation of a single charging station along the route: https://www.graphhopper.com/blog/2015/05/05/solving-the-elec...