As I understand it technically he is Superman's direct physical peer yes, with a 'but' attached to it... as the way his powers are granted and sustained means he is inherantly going to be variable.
Superman is kept stable and at an even performance level by his constant exposure to the Sun, Ultraman's power on the other hand is very different - being granted solely by regular exposure (or ingestion) of Kryptonite. Naturally then if he expends too much energy, or if he hasn't had access to Kryptonite in some time, he is weaker than Superman. On the other hand if he has recently binged on the green stuff, or if he has strategically implanted Kryptonite injections as he once did in Kurt Busiek's Justice League run, then he would be stronger that Superman.
If anything then a confrontation with Ultraman might well come down to a simple stamina equation - can the person in question match him long enough to tax his power and therefore begin to diminish it as he burns through his Kryptonite fuel...?