For a standard 5000-7000 kwh gasoline generator that produces 220-240V, does it matter if all the load is on a single 110-120V phase? Would it be better to distribute the load equally between the 2 phases?
Generally on a three wire unit, the rated load is at 240V. Only half the load is available on each 120V leg. It would be wise to balance the loads as much as possible.
There are new generators hitting the market now that somehow provide automatic load balancing on the 120V side. I believe it has something to do with how the rotor is wound.
Just as a nitpick, it’s going to be a single split phase, rather than two separate phases. There will be two generator windings each supplying 120 VAC, which are connected in series, in phase, to get 240 VAC. Typically, the connection between the two windings is tied to Earth ground and serves as the circuit neutral. You could tie either leg as the neutral, too, but it’s safer the other way, since the maximum voltage you’ll have WRT ground is 120 V, rather than 240 V.