who said that AM will beat PA? to you guys? who told you that lie? PA has a natural 50% dodge from a maxed out Blur and that can be increased to a 60% chance through butterfly. if you add on top of that an abyssal blade with its 3 second stun along with other heavy damaging items (and factoring in the pseudo RNG of coup de grace) a farmed PA will shred any and all fully farmed antimages.
Yeah, it's true. AM hard carries by farming a gold margin, then turning online with his big items and devastating the other team. If a PA has equal farm though, say through your team feeding her, she will usually beat AM.