Aside from protecting some people in the area near him in Italy, what we can fairly state is that he sure didn’t rise to the occasion in a proper Christian fashion.
The Israeli diplomat Pinchas Lapide credited Pius XII with saving hundreds of thousands of Jewish lives during World War II. (The specific citation provided on Wikipedia gives a range of at least 700,000, with an upper bound of 860,000.)
A particularly telling section with regards to why Pius XII was not more outwardly vocal, preferring instead to work in more clandestine fashion (underline is emphasis mine):
Pius XII followed the Dutch Roman Catholic hierarchy’s plan to name the Jews explicitly in their condemnation of Nazi deportations and intended to issue a similar statement himself. The Nazis threatened to arrest more Jews. The Dutch Reformed Church agreed not to protest openly but the Roman Catholic hierarchy issued, in May 1943 [sic; the pastoral letter in question was actually issued in April 1942, but was publicly reported on by the Jewish Telegraph Agency in May 1942], their famous protest against the deportations. The Nazis then launched an all-out offensive against Jews (except those who had converted to the Dutch Protestant Reformed Church). Ironically, it was the Dutch hierarchy’s letter of open condemnation which led to the arrest and execution of Edith Stein, the Jewish Roman Catholic nun and philosopher.
The news of the increased persecution reached Pius XII. His own protest was due to go into L’Osservatore Romano that very evening but he had the draft burnt saying “If the protest of the Dutch Bishops has cost the lives of 40,000 people, my intervention would take at least 200,000 people to their deaths.” (See II Seitimanale, 1 March 1975, p.40.) Such was the result of openly naming the Jews; more death from vain gestures.
Thank you. The evil was truly immense (and unfortunately it continues)