No, Memphis is much larger than Nashville. However, Nashville has the reputation as Music City, USA; which of course brings in the tourism and tourism affords metropolitan expansion. Statistically, Nashville is larger, but you have to consider that it is a 13 county metro area.
If I remember correctly from TN History in college; memphis, founded in 1819 and later incorporated in 1826, as a result of an accord between chickasaw Indian tribes and the powers that be. Later on in the 1840's when the capital was to be selected for the state of TN between several of our counties(White, Knox, Hamilton, and Shelby, I believe). During the time prior, Knoxvillem Nashville, and Murfreesboro played musical chairs as the host city of the TN government.
Memphis, being right on the Mississippi river, lost it's charter at one point, due to both bankruptcy and the Female Anophales mosquito(vector for malaria), due to the lack of people. This was one thing that knocked it out of the running for state capital. This economic uncertaintly made permanent Nashville's then temporary seat as Capital of TN. There were of course other factors such as the dispute over the geographic center of TN(Murfreesboro), water lines, prisons, legislative buildings, etc; but all that is for another post.
In summation, Nashville, while statistically larger in population is not larger than memphis; given the fact that the population collected is for 13 counties that make up the Nashville Metropolitan area.