matador,
I am not sure the rotor geometry causes changes in ground effect, since ground effect is almost purely the proximity of the blade to the ground, regardless of the type of rotor the blade is attached to. Than being said, there are big differences to how various rotor configurations handle in the hover, not due to ground effect, but to the hover itself.
Off the top of my head:
1) Downwash drag, or vertical drag - When the downwash hits the machine itself, it spends energy and also causes a down force that must be added to the total rotor lift. The vertical drag directly robs payload, and is different for different geometries. Tilt rotors and winged helos have the most vertical drag, with those big flat areas under the rotors. Most helos have 3 to 5% vertical drag penalties (a 10,000 lb machine spends 500 pounds) but a winged helo or tilt rotor often spends 10%.
A Chinook has higher vertical drag loses than a single rotor helo, mostly because the broad fuselage is under the tips of both rotors, where the downwash is highest, so the drag is more fierce. Tilt rotors are also burdened this way.
The ideal low-vertical drag machine has its fuselage tucked under the hub, and no broad parts near the rotor tips (look at the round, thin tail cones of the Mil products to see how they were influenced by minimizing vertical drag).
2) Rotor interference - When one rotor dumps its flow into another, the turbulent air is a problem for the lower rotor, and robs power/lift. A Chinook might lose 5% lift that way (enough to almost wipe out its gain due to having no tail rotor to rob power.) That is the reason for the big step-up of the aft rotor on a Chinook - in forward flight, the rotor wakes are seperated so the forward disk downwash passes under the wake of the aft rotor, and they never actually meet. A synchropter or coax might lose 10% power in a hover because almost all the lower rotor operates in air that was disturbed by the upper rotor.
3) tail rotor loses - Having no tail rotor is better for power, since the tail rotor eats about 5% to 7% of the total power.