Both. It's not just velocity, it's acceleration. At a given acceleration, velocity is strongly dependent on powder for a given charge weight and barrel length. The same approximate velocity can be achieved using a different powder with different acceleration, but the barrel harmonics may be quite different.
There *might* be if the burn rates for the two powder were very close. As noted above, similar velocity can sometimes be achieved with two different powders of significantly different burn rate due to the fact that acceleration in the barrel may also be quite different. If you use two different powders, but achieve the same approximate muzzle velocity by varying charge weight and differential acceleration, there is no guarantee that the barrel harmonics will be even close to the same, regardless of the fact that the bullets will ultimately be leaving the muzzle with approximately the same velocity. Quickload curves are a good illustration for this concept and QL can also be a very helpful tool to predict load behavior. However, sometimes the best/only way to really know for sure is to load some rounds and test them.