Once you move to full size sensor the lens has to cover much larger image circle and inevitably it shows in the corners.
Here is what SLRgear.com says about this lens tested on FF compared with APS-C:
quote:
Full-Frame Test Notes:
As always when moving from a sub-frame camera to a full-frame one, the 24-105mm lost a little sharpness in the corners, and chromatic aberration, distortion, and shading all got somewhat worse. That said though, corner sharpness and CA were both much better than most zooms we test, and stopping down to just f/5.6 made dramatic improvements in sharpness. Worst-case chromatic aberraton did increase noticeably, but the average CA levels remained very close to those we found on the 20D body, once again suggesting that the worst CA is limited to a relatively small area around the edges and corners.
The bad news with this lens comes in the areas of distortion and shading (vignetting). At 24mm, barrel distortion increased to a very noticeable 1.2%, while the pincushion distortion from 50-105mm jumped to 0.5% (also very noticeable, we personally find pincushion much more obtrusive than barrel, although neither is exactly welcome). Light falloff took a huge jump, reaching a level of more than 1EV at 24mm and f/4, and decreasing only gradually as we stopped down. At longer focal lengths it was less, but still on the order of 1/2 EV wide open.
While this is an exceptional lens on sub-frame cameras it falls to merely "very, very good" on full-frame bodies. The good news though, is that this lens is well supported in DxO's Optics Pro software: As of this writing (in late July, 2006), profiles are available for the 124-105mm for the 1Ds, 1Ds Mark II, and EOS-5D, as well as for the EOS-20D and 1D Mark II and 1D Mark II N. We haven't run our test images through Optics Pro, but venture to guess that much of the distortion, vignetting, and CA will be handily dealt with, not to mention most of the softness in the corners.
Bottom line, the Canon 24-105mm f/4 L is a really excellent optic, but one that struggles a bit along the edges and in the corners with full-frame bodies. As such, it's an almost ideal candidate for use with DxO Optics Pro, particularly if you're shooting with a full-frame dSLR.
unquote
It is worth looking at their review and sharpness graphs for both APS-C and FF:
http://slrgear.com/reviews/showproduct.php/product/145/cat/11
http://slrgear.com/reviews/zproducts/canon24-105f4/tloader.htm
http://slrgear.com/reviews/zproducts/canon24-105f4/ff/tloader.htm
The bottom line is that if you need a lens to be tack sharp in the corners of the full frame then you should probably used a high quality prime at F5.6 or F8.
You need to tackle other issues though e.g field curvature. If you use the central AF point on an object and then recompose with the object in the corner, then the object will end up in front of the plane of sharpness assuming your lens has the correct flat plane of sharpness. Simple geometry, but people forget about it.