Well if you're talking illusions that have some physical reality (and by physical I mean directly affects one or more senses, the most common being sight) then you'd go by intuition, as that's the attribute one uses to notice among other things discrepancies in their surroundings. Those created purely in the mind (a la Hallucinations), would require a check against the Psyche. I'd say that'd apply even to magical illusions that affect the senses as while they're produced by magic they aren't really affecting the mind of the character so wouldn't in that case do a Psyche check against the magic but use Intuition instead. A good example of that would be Mephisto, as it was established during the Secret Wars II that his influence on the earthly plane is totally illusionary and you'd need an Intuition feat to see through them I'd say in that case.
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