My vote goes for the 300/4 IS....
But I'd suggest you go ahead and get a 1.4X to use with it, too. To shoot wildlife, particularly with a full frame camera, you will need more than 300mm reach.
300/4 IS with EF1.4X II.....
The 300/4 IS is little larger than your 70-200/2.8. But not much.... it's still very hand holdable and portable. It also uses the same 77mm filters, so it can share any you might already have and use. However, I'd note that this lens "doesn't like" filters. A protection filter on it will cause quite a bit of image quality loss (though not as much as one on the EF 100-400L).
The 300/4 was was one of the very first lenses to get Image Stabilization, so is an older design. It might not be the latest and greatest IS, but it's still helpful and works. It's IS is probably worth 2 or 3 stops, where you likely see 3 or 4 stops assistance with your 70-200. Like your lens, it's got Mode 1 and Mode 2 IS, and a focus limiter.
One thing, if using the lens on a tripod, locked down so that there's no movement, this is one of the lenses where IS needs to be turned off or it can go into sort of a feedback loop where it actually causes movement! Your 70-200 has a more sophisticated form of IS (as do all the Canon 70-200 with IS), that self-detects lack of movement and shuts itself down when not needed. I use the lens primarily handheld, occasionally on a monopod (for the black tail deer shot above) and on the rare occasion when I put it on a tripod, it's on a loose gimbal mount to allow following moving subjects... so I really can't recall ever turning IS off on my copy of the lens.
A minor characteristic of this lens is that it tends to add a purple tint to specular highlights. I've seen this with other lenses and think it's due to a certain type of glass used in the lens. It really isn't a problem, it's easily fixed in post-processing, if at all. It's present in eye catchlights of the above hawk shot, but doesn't bother me so I left it alone. Here's a tight crop from the image showing the effect....
Another popular Canon lens you may want to consider for wildlife is the EF 400/5.6L. It's very sharp too, and yet it's still quite portable. Unfortunately it doesn't have IS and as an f5.6 lens, adding any teleconverter to it (even a 1.4X) will cause it to not auto focus on your camera (there are sneaky ways to get it to try to focus, such as taping up a couple pins on the TC, but it still will be slow and hunt more). Personally I prefer the 300/4 and 1.4X TC over the 400mm lens, since the 300mm works so well with a TC that I get two very useful focal lengths, instead of just 400mm.
I shoot a lot of sports and less wildlife. About 90% of the time I'm using a pair of crop cameras (7D) and my most used lenses are 70-200 on one and the 300/4 on the other. Above images, however, were both shot with the 300mm on 5DII.
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Alan Myers
San Jose, Calif., USA
"Walk softly and carry a big lens."
GEAR: 5DII, 7D(x2), 50D(x3), some other cameras, various lenses & accessories
FLICKR & PRINTROOM
Just a point, if you have a 400mm lens with a 1.4x extender on a 1D Mk IIn, your efective focal length is 728mm.
Not 560mm. With the 2x installed it would be 1040mm. This is some serious focal length! 
