It's a good question whether Henry Paulson showed favoritism to Goldman Sachs, but we need evidence to make a judgment about the answer. The rest is speculation about a hypothetical person's choices and their outcomes in a highly complex, chaotic, novel situation.
Most experts, especially those within the establishment, say that allowing all those institutions to collapse would have been catastrophic and that the government should have rescued them. I think it's reasonable to expect that if one of those establishment experts was the alternative to Paulson, a likely scenario, then they would have acted similarly.
If someone acts to prevent catastrophe and succeeds, critics always can (and do) say that the catastrophe wouldn't have happened anyway.