Generally for Battery Charging purposes it does not really matter "that much". The trick is to ensure the genset can stay within the correct frequency range (57-62hz) for North American power compatibility. 47-52hz for EU.
If your Inverter/Charger is also doing Pass-Through power to "house AC" while charging, then you will get Mod Sine passing through and THAT isn't good. Motors (fridge compressor , water pumps etc) will strain with Mod-Sine and of course there are electronics issues too that can arise.
IF possible, it is best to use a Pure Sine Inverter Genset, especially if you are using Pass-Through AC and running equipment that may be affected by less clean wave forms such as Mod-Sine.
I am not aware of any modern Generators using Square Sine (that s REALLY bad), they are typically Mod Sine or Pure Sine (Inverter generator).
AN ASIDE: If using a Generator to charge, pending on charger capacity.
My Inverter/Charger (Samlex) can deliver 100A Charge to 24V bank (programmable) but that only pulls <33A / <3800W at 120V.
I think I can select the source in my unit. I have to look & I am slammed. But basically if I am thinking correctly, I can tell the unit to use the battery always. So it would not be passing AC through.
I rented a 2000w generator for the weekend & when my compressor would turn on the compressor would over draw fault. I had to keep restating. Thats why I was thinking about the settings. Just haven't had the time to play with it.
I have some more generator related questions I'll start a new thread for.