The kamon (family crests) made me immediately think of urns for ashes, but the markings don't show anything that might further identify it as that kind of urn. And the "吉日" (lucky day) makes me think its definitely not an urn. I would also expect to see a posthumous buddhist name on the urn (a long, maybe 7-character name) if it was meant to hold ashes.
The address on the big urn
本所区中横町會 Honjo-ku, Nakayoko town association
is a local community association, still common in towns and neighborhoods in Japan. So this, too, makes me think its not a funeral urn. Plus, it seems to be a crude engraving, as if it were done by an amateur. So I'm thinking it is a trophy for a local event.
The four kanji on the taller vase are a mystery. Names? Nicknames?
相亀 Aikame?
音壹榮 Shōei?