Generally in game systems, I like all sides to be playing by the same rules.
It bothers me on some level when they don't.
A lot of my gripe comes from playing video games, to be honest. Too many strategic games where re-supply is critical, but the computer doesn't play by the same re-supply rules, so you waste time trying to wage economic warfare or cut off units. Games were ammo is crucial but the computer doesn't run out of ammo. Games were the computer gets a weird bonus to its units, so you can't rightly predict combat power. Games where the NPC version of an identical unit is more powerful - and it loses said power if you somehow convert it to your side. Games where the enemy gets unlimited spells, or arrows, or tanks, or access to (when controlled by a human) command-and-control limited units . . . I feel like I'm getting things slanted against me in a way that prevents me from using my cleverness (and luck, to be fair) to win.
In RPGs I'm a bit more forgiving. I can shrug off intentional one-sides rules - the dark vision of monsters, and the ways doors open for them, in the original D&D books. That's just the environment playing against you. I don't love them, but there we are.
I'm totally fine with the NPCs (or the PCs) getting access to rules and abilities that the other side doesn't. That seems essentially fair to me. After all, games were some races, choices, equipment, etc. is limited is the bedrock of gaming for me. I'm fine with GURPS PCs being built with points and monsters not being built with them (since the budget is unlimited, anyway, why does the total matter?) They're using identical rules - Unkillable might be off-limits for PCs in this game but the monsters use it the same way as the PCs would if they had it. If they both have Night Vision 5 or Weapon Master (Rapier) they both use it the same way. Access doesn't need to be level or fair, just effects and rules, for me to feel like "the same rules for all" applies.
But I don't love it when games, say, have PCs in levels and classes and NPCs in HD. I don't love it when the NPC version of something doesn't match the PC version. It feels more complicated that necessary, like more things to learn and know, and I just feel it's a sub-optimal decision. And it just bothers me.
I'm curious how others feel when they encounter this.