The transverse momentum (p(T)) spectra and ratios of identified charged hadrons (pi(+/-), K-+/-, p, (p) over bar) produced in root s(NN) = 200 GeV Au + Au and d + Au collisions are reported in five different centrality classes for each collision species. The measurements of pions and protons are reported up to p(T) = 6 GeV/c (5 GeV/c), and the measurements of kaons are reported up to p(T) = 4 GeV/c (3.5 GeV/c) in Au + Au (d + Au) collisions. In the intermediate p(T) region, between 2 and 5 GeV/c, a significant enhancement of baryon-to-meson ratios compared to those measured in p + p collisions is observed. This enhancement is present in both Au + Au and d + Au collisions and increases as the collisions become more central. We compare a class of peripheral Au + Au collisions with a class of central d + Au collisions which have a comparable number of participating nucleons and binary nucleon-nucleon collisions. The p(T)-dependent particle ratios for these classes display a remarkable similarity, which is then discussed.