Once painted, any small differences between textures are moot. The diffraction offered by different textures might be a factor, but again a very small one.
Given the issues presented by "popcorn" type textures, which have just been demonstrated following water damage, it's hardly worth messing around with.
A few absorption panels attached to the new ceiling would offer a great deal more benefit. But, if the rest of the room is adequately treated, it's still a relatively small benefit. Worrying about just one of six surfaces is mis-directed energy.