I've talked about this before in other threads, but because I use the Variant rules for aligning a skill to any ability score depending on the situation... I use both WIS and INT for Perception and Investigation. WIS is used for the Passive use of both skills, INT is used for the Active use of both skills. Perception is used for the detection of any living thing that is trying to hide-- anything that moves around, makes noise, can make tracks etc. Investigation is used for any non-living hidden thing-- traps, secret doors and so forth.
If someone has used Stealth to hide, you'll notice him using Passive Perception (10 + WIS + Perception). To notice a tripwire across a hallway automatically uses Passive Investigation (10 + WIS + Investigation). If you use an Action to search for someone who is hiding, that is Active Perception (d20 + INT + Perception). If you use an Action to search for a secret door or trap, that is Active Investigation (1d20 + INT + Investigation.)
This has worked very well for my tables, and my players always know which ability scores and which skills apply to which situations.
If someone has used Stealth to hide, you'll notice him using Passive Perception (10 + WIS + Perception). To notice a tripwire across a hallway automatically uses Passive Investigation (10 + WIS + Investigation). If you use an Action to search for someone who is hiding, that is Active Perception (d20 + INT + Perception). If you use an Action to search for a secret door or trap, that is Active Investigation (1d20 + INT + Investigation.)
This has worked very well for my tables, and my players always know which ability scores and which skills apply to which situations.