New measurements by the PHENIX experiment at the Relativistic Heavy Ion Collider for. production at midrapidity as a function of transverse momentum ((PT)) and collision centrality in root s(NN) = 200 GeV Au + Au and p + p collisions are presented. They indicate nuclear modification factors (R-AA) which are similar in both magnitude and trend to those found in earlier pi(0) measurements. Linear fits to R-AA as a function of (PT) in 5-20 GeV/c show that the slope is consistent with zero within two standard deviations at all centralities, although a slow rise cannot be excluded. Having different statistical and systematic uncertainties, the pi(0) and eta measurements are complementary at high (PT); thus, along with the extended (PT) range of these data they can provide additional constraints for theoretical modeling and the extraction of transport properties.