Mirror clearance is less with a full frame sensor camera
Many lenses that work fine on an EF-S mount camera will not work on a full frame sensor camera because they extend too far into the camera.
As the camera’s mirror swings upward, the distance between the edge of the mirror and the lens mount decreases. When the mirror is down on an EF or EF-S mount camera, the edge of the mirror is 16mm behind the lens mount. When the mirror is up on an EF-S mount camera, there’s 12mm of space between the mirror and the lens mount but there’s only 6.5mm of clearance on a 5D Mk II.
Mirror clearances are not an issue with mirrorless cameras which allow you to use a larger selection of lenses because of their low FFD.
Testing for mirror clearance
An old Canon film camera is a good test camera if you have the 5D Mk II. Focus the lens at infinity, where the rear element is closest to the mirror, and trip the shutter. If the mirror hangs up on the lens, remove the lens, let the mirror fall back into place and don’t use the lens on your full frame sensor digital camera.
A rear lens cap with a hole cut in the bottom can also be used to check the mirror clearance for a particular lens. Set your lens to infinity and measure from the inside of the lens cap to the highest point on the lens. Subtract that measurement from the the depth of the cap and you’ll know how far the lens extends into the camera.