Re: Pyramid Head vs Nemesis
(The following comes from someone who has never played either of the series in which the characters appear. I have read the wikipedia entries for both characters, read some of the Resident Evil wiki and watched the first Silent Hill played through in a let's play, though.)
Tie.
In one interpretation, Nemesis has no issues for Pyramid Head to be spawned from, so if you think of Pyramid Head as being psychological, the fight cannot occur. In another interpretation, Pyramid Head can is a normal monster and Nemesis wipes the floor with him. The only interpretation I can think of that lets Pyramid Head be his full self and also able to attack Nemesis, is if Silent Hill's god is born. This would mean the Silent Hill 'otherworld' would be made manifest, and Pyramid head would exist without the need for a host to live off.
Pyramid Head seems to be unkillable while existing from the trauma suffered by it's host, I'm going to assume that this immunity carries over when in the real world. It would not be unreasonable to assume that he is powered by the unending trauma of all the souls his god has taken. Even if he were blown up, Pyramid Head would continue to exist and likely respawn. The god is immune to all forms of damage except this one chemical, probably made up for Silent Hill, so Nemesis likely doesn't have any. Without the ability to kill either Pyramid Head directly or the god allowing him to exist, Nemesis is unable to do anything permanent about Pyramid Head.
Nemesis cannot be killed by Pyramid Head since, AFAIK, Pyramid Head only has the bigass knife and pointy hat to fight with, while Nemesis' regen lets him survive anything short of a railgun and be up again in moments. In other words, neither of them can actually kill each other, so the contest is a draw. That being said, Pyramid Head is 'more invincible' than Nemesis, who -can- die, whereas Pyramid Head will effectively continue to exist, 'as long as there is mental trauma'.
...At least, that's how I see it.