Is this a symptom of a bad cell?

Or possibly just sulfation?

My '73 Plymouth does not get driven that often and over the last couple months I have been experiencing some battery problems.

It usually takes 15-20 seconds of cranking to get gas back up to the carb when it's cold, and the starter will spin fast for maybe 10 seconds, then slow down, as if the battery is going dead. However, it will spin the engine in that "reduced charge" condition for quite a while. It does not just go down to nothing in one whack. After the engine starts the ammeter shows a significant charging level for a while as if the battery were deeply discharged.

Warm starts are fine since the engine needs only a few revolutions to start. Battery connected or disconnected between drives makes no difference so it isn't a drain. Alternator is charging well. Just curious what goes on with batteries when they lose their "surface charge" prematurely.