The 20 kW head, loaded at only 3 kW will be less efficient than the 3 kW head at the same loading. Two reasons: Bigger fan and bearings causing more friction, and a larger magnetic 'circuit' requiring more field excitation. The efficiency of these machines will usually peak at maximum load.
Another, not-so-obvious drawback is the larger machine's rotational inertia will put higher peak loads on the belt. The reason is that the Listeroid speed varies throughout its 4 stroke cycle, even at zero electrical load. So as the engine slows during the compression stroke and speeds up during the power stroke, the belt is being alternately slackened and tightened. The more mass you are spinning in the alternator, the worse this problem becomes. It has been the cause of some frustrating belt issues in my power plant project of late.
I like the idea of oversizing the generator a bit, but it does come at a cost.