It looks like Karen has misinterpreted. Gollum speaks of days and months at the Black Gates. That sounds to me like he was referring to the Siege and the War as a whole.
It's probable that the Battle at Dagorlad was fairly swift. The description of Gil-Galad, Aeglos, and the might of the Numenoreans implies that the good guys routed the baddies.
And Gandalf's words about Ancalagon mean nothing because, as has been suggested, the Hobbits might have heard of Ancalagon and not Glaurung. Maybe Gandalf himself had told a young Frodo about Ancalagon.
Ancalagon was mightier, for the reasons stated previously.
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