Iron Man is correct that one radar being AESA and one radar being PESA does not automatically suggest that the former is superior to the latter.
However there is no public indication, nor little theoretical reason to imagine that Type 346 lags SPY-1x in any respect, including supporting software. Immature software support may have been relevant in the early days of Type 346, but at this point we are more than a decade on from the system's first fielding on 052C.
There are diminishing returns in software development -- the task of tracking, intercepting targets is not an open-ended problem -- and I suspect we are well past the point where the greater "maturity" of vanilla Aegis is outweighed by the inefficiencies and bootstraps required to maintain and extend aged software architecture.