I've managed to greatly improve the braking feel of my 6700 lever. I'd read that the 6700 (and 7900) levers have a different cable pull ratio in different parts of their sweep (I believe Shimano call this feature Servo Wave). I therefore released a bit of cable at the brake caliper, which meant that the bite point (where the brake pads first touch the rim) is now when the lever is a bit closer to the handlebar. This made all the difference! There is a lot more modulation and a lot more power available, and it now feels pretty similar to how it did with the 6600 lever.

I still don't fully understand all of the geometry/mechanics involved, but I do have a lever with a feel that I'm now happy with.