Limenitis archippus.
Danaus plexippus.
Viceroy pictured first. The black band across the hindwings is the most obvious field-mark difference. In the Southwest, however, this band can be faint or even missing. The Viceroy is also smaller than the Monarch, which is one of our largest butterfly species. This Viceroy was seen, along with a couple of others, and some Monarchs, at the Shawangunk Grasslands NWR in Ulster County, NY. I’ve never seen one in Brooklyn. There are four Brooklyn (Kings Co.) records in iNaturalist, three from 2017, one from 2018. Butterflies and Moths of NA has one record, from 2017. Why so few? Willow, aspen, and poplar are their larval foodplants. But they like “wet meadows, edges of watercourses, and other open wet habitats” (David L. Wagner, Caterpillars of Eastern North America), not common here.
Red-spotted Purple (Limenitis arthemis) included here because, come on, this picture!, but also because they are in the same genus as Viceroys.
Viceroys famously mimic Monarchs. It was originally thought they just looked like Monarchs, which are distasteful to many predators because of the milkweed sap (latex) they eat, but there is now some thought that Viceroys also taste horrible as well. In Florida, the Viceroys are redder, mimicking Queen (Danaus gilippus) butterflies.