This issue caused a lot of controversy when British builder Paul Hopkinson originally shared this video on Costa Coffee's Facebook page.
Responses ranged from angry (and very British) to extremely pragmatic. Costa coffee themselves also responded to point out that the larger cup has space at the top and if the smaller cup did too that would equal the difference in size AND that the larger cup has two shots of espresso as opposed to one.
via Paul Hopkinson
As for the engineer's math, we're going to take his word for it and assume that he's solved the mystery of why both cups seem to hold about the same amount of liquid.