Slightly leaning forward can cause a lot more back pain than fully leaning forward and for many people (non pro athlete types) is less efficient than either fully forward or bolt upright.

The best riding position for back, neck, and shoulders is fully upright Dutch geometry. This aligns your sit bone, spine, and neck, places weight properly on your sit bone, and takes weight off your palms and shoulders. This is one reason that places like The Netherlands and Sweden sometimes seem like giant old folks homes. It's not that they have more old folks (though they do slightly due to longer lifespans) but that the bikes they're riding (and the protected bikeways) allow them to continue riding until the day they die (and a significant bit of their bicycle fatalities are old folks having heart attacks or strokes and crashing).

Note that many bikes that purport to be Dutch do not have the proper geometry. Electra in particular will often cause more back problems than just about any other bike due to the seat being too far behind the bottom bracket and head tube. The same goes for cruisers and similar bikes.

More: City Bikes | LocalMile