If you stick to metro statistical areas (a smaller geographical area), Charlotte's is surprisingly about twice that of Raleigh: 2.95 million vs 1.6 million. If you use combined statistical areas, which are a better measure, it's 3.5 mil vs. 2.5 mil. Raleigh still has a lot of catch up to do to get to Charlotte's size.
By comparison, the Nashville MSA is 2.2 mil, and its CSA is 2.5 mil. So Nashville is smaller than Charlotte no matter how you measure, it has a more concentrated urban core than Raleigh, and it's the same size as Raleigh if you count the surrounding areas.
This is still gonna come down to the battle of billionaires, though, imo.