A MOS diode will have zero recovery time because it is all
majority carrier (provided you don't push any of the parasitic
diodes into forward conduction). They also can be gate-
commutated making them "more ideal" - important when you
are dealing with signals of very low amplitude that might not
even ***** a PN diode "on".
"Freebie" diodes often have unfortunate size, connectivity
limits and tend to not be characterized very well for stuff
like reverse recovery time (which could allow most or all of
your forward-harvested-charge to slosh right back out of
the reservoir).
A diode which has both terminals "free", in a JI process, must
be in a well (or nested wells). This means it's really a BJT that
you hope stays in cutoff, and has large stray capacitance at
some (possibly invisible) "terminals".
You should have at least two types of possible, zero cost but
fairly poorly modeled and controlled, diodes in any JI CMOS
technology. There may be "better" ones in a twin-well flow,
but whether these are actually better for the use, you'd have
to judge for yourself. The extra well is extra cost, of course.