These test images were shot using and EOS 40D and are 100% crops from the original JPEG images, with no post-exposure sharpening. The EF 100-400/4.5-5.6L IS USM, the EF 300/4L USM and EF 70-300/4-5.6IS USM lenses were used. They were shot with the camera/lens on a tripod using a remote release and mirror lock up. I'm showing the "real world" images because I think they provide a better visualization of the relative image quality you can expect when using the lenses. The "pattern" is actually the fabric of a lawn chair, but it contains a lot of fine detail which makes it a good target. I also shot a series of resolution targets at the same focal length settings. The results of the two sets of images correlated well, with the resolution test target shots being a more sever test and showing aberrations which aren't really apparent in real images. When I couldn't tell which was the better real world image, I used the test target shots to make the final decision.
I'm not going to post many images here because both the 100-400IS and 70-300IS show high image quality both in the center and at the edge of the image. Just as an example, here's a comparision of the edge at 200mm. There's even less difference at 100mm and in the center. Since there's no real detectable difference in these real world shots at the edge at 200mm, there's little point in showing other images.
Looking at the resolution test charts and pixel peeping, the 100-400IS did was slightly sharper at 200mm and at the edge of the image, but the difference was pretty small and unlikely to be noticable.
All three lenses reach 300mm without addings a multiplier. The 100-400IS and 70-300IS both have a maximum aperture of f5.6 at 300mm. The 300/4L has, of course, a maximum aperture of f4.
In the center of the frame at 300mm all three lenses are very good. The 70-300IS has perhaps slighly lower contrast, but you can't really find fault with any of them. Stopped down to f8 the 70-300IS is closer to matching both the 100-400IS and the 300/4L.
At the edge of the frame the 300/4L holds very high image quality, almost as good as the center image quality. The performance of the 100-400IS at the edge is still quite good, but not as good as in the center and not as good as the 300/4L. It improves quite a bit when the lens is stopped down to f8. The lens that suffers most is the 70-300IS. The image has lost contrast and some sharpness. Though not immediately evident from the images above, the 70-300IS is also starting to show a little chromatic aberration at the edges
The lens of choice at 300mm is the 300/4L because it's a full stop faster than either of the other lenses and has better edge quality. Second choice is the 100-400IS and third choice is the 70-300IS because it's image quality at the edge of the frame can't quite match either of the other two lenses.
The 100-400IS reaches 400mm at f5.6, while the 300/4L + Canon 1.4x reaches 420mm at 5.6 and the 70-300IS with the Tamron 1.4x reaches 420mm at f8. The following images were taken from the same position, so the images made with the 1.4x multipliers appear slightly larger. I think this is a fair comparison though, since that's the way these lenses would likely be used. i.e. shooting from the same distance. First let's look at the center of the frame:
As you can see, there's very little difference between the 100-400IS and the 300/4 + 1.4x TC. Both give excellent images with good contrast and sharpness. Both are a little better when stopped down a stop then when shot wide open. The 70-300IS +1.4x TC shows a drop in contrast and sharpness compared with the other two lenses (and it's a stop slower), so it definitely comes in last when shot wide open. However it improves quite significantly when stopped down a stop to f11, to a point where it's almost holding it's own against the larger and more expensive lenses. Don't forget though that it's manual focus only with the TC, which makes operation much slower and very difficult if the subject is moving.
Image quality at the edge of the frame (even an APS-C sized frame) is lower than in the center of the iamge, especially in the case of the 70-300IS + 1.4x. Even stopped down to f11, the 70-300IS image is lacking in sharpness and contrast. The 100-400 and 300 + 1.4x are pretty close in sharpness and contrast on this "real world" taget viewed as a 100% crop. However in tests using resolution targets and looking at 200% crops the 300 + 1.4x shows more chromatic aberration and perhaps a touch less sharpness. So in the real world it's probably a tie, but if you pixel peep closely enough, the 100-400IS just wins out in image quality at the edges of the frame.
These images show the 100-400IS with a Canon 1.4x TC and the 300/4L with a Canon 2x TC. I didn't test the 70-300is with a 2x for three reasons. First, I don't have a 2x that will fit it , second the performance would be expected to drop to the "unacceptable" level anyway and third, manual focus at f11 isn't a lot of fun.
With the 100-400IS, the 1.4x TC takes it to a manual focus 560mm f8. There are ways to "fool" the camera into AF by taping off some of the pins on the back of the lens, but if Canon don't think AF is reliable at f8, who am I to argue! To play safe I used manual focus. The 300/4L with the 2x TC becomes a 600mm f8, again manual focus. To make sure focus was good I used an eyepiece magnifier to assist. Focusing without it is possible, but is easier with it. Again I shot form the same position, so the 600mm image scale is slightly larger.
Looking first at the center of the frame, it's evident from the shots wide open (in both real world and resolution chart tests) that the 300/4L contrast wide open with the 2x attached suffers quite a bit. The image isn't as good as that obtained using the 100-400IS + Canon 1.4x TC, so if you want to shoot at f8, the 100-400IS is the winner (though also 40mm shorter). The differences are even more obvious on resolution chart test, but unless you're going to be shooting resolution charts, the real world results are more relevant. Stopped down a stop the 300/4L + 2x image improves significantly and there's no significant difference between the lenses.
At the edge of the frame both lenses show some drop in contrast. Again the 100-400IS + 1.4x has the better image wide open. Stopped down a stop (to f11) both lenses improve to a point where their performance is pretty similar. The 100-400IS + 1.4x does show a little less chromatic aberration and slightly higher contrast, so I'd have to say it's the technical "winner" here.
With a 2x TC on the 100-400IS you can get an 800mm f11 lens. Definitely manual focus only under these conditions and the image at f11 isn't very bright, but accurate focus is possible if you take care. Again and eyepiece magnifier helps.
At 800mm image quality isn't impressive. It's not too bad in the center of the frame stopped down a stop, but an 800mm f16 lens isn't really all that practical most of the time. In good light with a static subject, time to focus and a stable tripod (and perhaps mirror lock up), you can certainly get images that wouldn't look too bad at print sizes up to 8x10. A little help from photoshop to increase contrast and sharpness can also do wonders. So in a pinch, it's a usable combination, but it's not something I'd want to try to use very often.
When using a 2x the question is often asked "Is it better than just upsizing the image shot with a 1.4x TC). Well, below are two images. On the left is a 100% crop from a shot with the 100-400IS + Canon 2x TC. On the right is an upsized image (140% crop) from a shot with the 100-400IS + Canon 1.4x TC.
Not a huge amount of difference.