Why are these two electrolytic capacitors so hugely different in size?

Alotta empty air... Those are very old designs (60's), one might use them to restore vintage equipment w/o affecting their appearance.

https://www.lespaulforum.com/forum/showthread.php?177151-Sprague-TVA-Atom-vs-Nichicon-VX-Series

Guitarists and audiophiles spend stupid money chasing "tone", thinking there's some sort of magic in the parts themselves.

Generally speaking, manufacturing has changed significantly since the old Sprague caps were designed, so unsurprisingly there's a lot of blank space in that case. Aluminum electrolytic capacitors can have same specs / be different physically due to a few factors, including lifetime, mechanical robustness, and designed specifically with ESR/ESL in mind. Different electrolytes, layer thickness, encapsulation, electrolyte volume, venting, etc. can all be tweaked to make a component for a specific application. Audio capacitors, You would definitely need more of the electrical specs to know why two "equivalent" caps would be different sizes.