I always liked the idea of "Psionics-magic translucency," where they're sorta similar but not really.
Essentially, checks to overcome resistance of the opposite type roll twice and take the higher roll, due to it sorta kinda working to resist the wrong kind but not really,
Dispel Psionics works on magic effects if the Manifester rolls higher on a Manifester level check against 10+ level of the spell used to make the effect + caster's key ability mod, and vice versa
Psionics can work in AMFs, but 50% chance it simply fails, and vice versa
Detect Psionics can detect sources of magic, but it never goes past the information gained from round 1 for detecting magic, and vice versa
Or, just roll 50% automatic failure or success if the types collide, if that's easier. Obviously feats and skill checks remain completely opaque and different.
My DM pulled this on us in our most recent campaign, and it worked quite well. It didn't exactly help keep everything balanced, per say, but it did make the world feel a lot more alive.