Vaux's Swifts from above
Chimney Swifts from above
Chimney, note the longer tail and less contrasting rump. The wings are longer and the bird larger as well .
Vaux's, note the short tail and more contrasting rump. This bird was mounted in an unnatural position with the wrists pulled back.
Here's the two together. Note the larger Chimney with the longer tail, and the smaller Vaux's with the shorter tail. And the rump coloration, again more contrasty in the Vaux's.
Chimney Swifts from below
Larger Chimney, smaller Vaux's. Not sure what subspecies these are, that may account for the browner coloration of the Vaux's.