I need some more synonymous constructions for equal, identical, the same in context such as Models A and B performed essentially equal on task X. Is on par a valid replacement for equal/ identical/ the same here, or is on par only suited for informal contexts?
Here's an example from The United States Surgeon General's Report in 1999:
It is a work of real significance, on par with the Surgeon General's historic first report on smoking and health published in 1964.
This was justified by the functional difference between the father and the mother of an illegitimate child in case of absence of a family; the mother is then responsible for personal care, which is on par with financial support, but the father can ...
In neither of these cases is it seen in a "colloquial" sense; rather, it's seen in a serious, not to say sobersided, publication.
Note, however, that it has only recently come to the fore—and not quite to the fore, really, since the synonymous phrase "commensurate with," though in decline, still eclipses it by a wide margin.
Edit, thanks to Tim Lymington:
As Tim correctly notes, "on a par with" is much more common than "on par with." It's essentially the same usage, though, and occurs in such non-colloquial works as a translation of Aquinas's Summa Theologicae.
Just to clear out a common misconception beforehand: as opposed to many people's claims, "par" does not originate from golf. "Par" is a loanword from Latin that means "equal" and the word itself is used in most of the Latin languages (and also in Dutch as "paar") to signify 2 equal things, a pair.
For the "on par" expression: according to the Cambridge Dictionary "on par" is a standard (not colloquial or technical) and is listed as a common expression in Business English, as well as the derived expression "subpar" meaning "below average" or "below expected standard".