as CP said pf is what is demanded by the load and supplied by the source (generator).
This pf (or rather the reactive power portion) is shared by the generators - whether equally or unequally depends upon the reactive droop compensation.
You may check details about this. There are several control modules where this feature exist for example check here.
run first one at about 30% rated current leading zero power factor.
the second at 30% rated current lagging zero power factor.
and have zero current actual load.
This you could get by reducing excitation of first generator to zero.
The effect of low power factor, compared to unity power factor, is unnecessarily high operating temperature of generators (reduced life) and energy losses.
As has been written by other posts, the load power factor cannot be changed.
So, if you run one generator at unity power factor, and the load is 0.8 power factor, the second generator has to run at less than 0.8 power factor IF the kilowatt (real power) load is shared.
But I am not sure if you meant to write "effect on power factor" or "effect of power factor".
I believe this document addresses your question perfectly. There is also a link within the PDF to help you size your genset.
The generator does notset the pf in any way shape or form any more than your utility sets the pf for your facility, but must be able to hold the load at a rated power factor.