I do know that efficiency on higher gravity batches tends to be lower. I don't know why this is though.
This is because the amount of wort lost to the grain bed is directly proportional to the amount of grain.
Assuming complete conversion of the starch in the grain bed, efficiency is then due to lauter efficiency. For a batch sparge, lauter efficiency is then dictated by volume lost to the grain bed and dead volume, as well as some technical details like stirring the sparge to evenly distribute the sugars in the sparge water.
Fly sparging is more dependent on tun shape and design, primarily because the tun needs to be designed to allow even flow through the grain bed. That means that the manifold needs to be designed correctly for the shape. A deeper grain bed will tend to be more efficient for fly sparging because more water will pass through each grain kernel on the way to the outlet, but be essentially irrelevant to batch sparging.
Another potential variable between two tuns is that one might maintain temperature better than the other. Loss of heat can decrease gelatinization and slow down conversion