In the load sharing circuit it's assumed the charging source is ultimately mains powered, so dissipating a little heat in the diode doesn't really matter. But the mosfet switches the battery with very little drop.
If I read the datasheet correctly, you can have both ENables turned on all the time, and the highest voltage source will always power the output. I don't think you have to invert one of the enables because it says the diode has to be forward biased to conduct. So if V1 is higher than Vbat, then it would always power the output if it's plugged in, even if both diodes are enabled.
It also says you need capacitors on input and output which you wouldn't need in the load sharing circuit. And there would be some current needed to power the diode logic when running on battery - a few microamps which you wouldn't have with the plain load sharing circuit.