Whichever comes first.
PHB, page 203, Spellcasting, Duration, Concentration
If a spell must be maintained with concentration,
that fact appears in its Duration entry, and
the spell specifies how long you can concentrate on it.
The duration listed is the maximum allowed amount of time one can concentrate on that spell. In my interpretation, this is essentially saying that after 1 hour, you will fail any concentration check due to the intensity of the spell.
One possible ambiguity is when the magical act in question isn't explicitly a spell. The question you referenced is about an alchemical procedure, and the confusion there is over whether or not the time limit begins when the procedure is started or the procedure takes effect. There is no such ambiguity with spells, as the spells duration is measured from when the spell is completed and takes effect.