Peterson wasn't even close to Tatum's refinement. Peterson was flashy but his style of playing was mostly based on blues patterns adapted to the emerging style that be-bop was at the time. Bud Powell was also influenced by Tatum but was a much greater pianist then Peterson. Tatum's influence can even be heard in McCoy Tyner's work.
Peterson brought his own style to the scene....no one is comparable to tatum, but Peterson swung better than anyone else in my opinion, his licks were like any other, peterson was just very unique