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:
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.
It is worth looking at their review and sharpness graphs for both APS-C and FF:
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.
It's not really an excellent optic for an L. Even my Tamron 28-75 which cost me 1/3rd the price (this was back then) was sharper even center frame. At the wide end the 24-70 II, 24-70 f/4 IS, 24 2.8 IS, 24 T&S II, 24 1.4 II clearly show that the 24-105 is pretty far from very, very sharp.
I don't what SLRGear is going on about how it does much better than most zooms on FF at the edges, when it does about the worst of any L zoom at the edges on FF and worse than some third party zooms at FF edges and it has nasty CA of both lateral and longitudinal forms. They also said the 70-300L (amazing) was basically worse than the tamron 70-300 VC and 70-300 non-L too remember, not that the latter two are bad but.
Maybe 1 in 25 are uber copies that are pretty good, but I've tried a few and all left me disappointed on FF (not bad on APS-C, but then again, I found even sharper for radically less back then, of course now that the 24-105 can be had for $500-650, for that price level it does perform reasonably well, especially consider the super wide range and IS and everything it brings all at once.)
+1! And the 24-105L I rented had tons of CA at the wide end, even on a 1.3x crop camera. That said, I'm considering buying one for my 6D. I think the overall color rendition, along with the zoom range, are the strongest points of this lens...and they're so strong that they seem to beat the competition if you consider all variables. There just is nothing else that covers this range, that is a zoom
, with IS...that compares...at this price level
...on a Canon mount. I also considered the Tamron 28-75, but it does not have IS, and doesn't seem to hold its value very well on the used market...where the Canon 24-105 does hold its value a bit better. For a new price in the $750 range...the 24-105 is just a terrific value. If you absolutely must have an f/2.8 zoom for the lowest price possible, then the Tamron 28-75 is the only choice.
For absolute optical performance at 24mm, it would appear from tests I've read...that the Tokina 16-28 has them all beat (at least up to f/4.0 or f/5.0, where the pricey Canon 24mm f/1.4 takes over, especially regarding resolution). The Tokina has a flare problem, but it might be worth trying anyway. It's possible the Canon 24-70 f/2.8ii has more resolution than the Tokina (at 24mm specifically)...I've not compared the tests directly yet. But price is an issue for me there...and also the Tokina would still likely have less barrel distortion than that pricey Canon...at least based on the tests.
For the wide end, I'm still torn between the Tokina and the Sigma 24mm f/1.8, because I want to do low light shots that have a lot more color than f/2.8 can provide. The Sigma is quite soft towards the borders and corners, but it's not much softer than the manual-only Rokinon, yet costs $50 less than the Rokinon.