Thought I'd post something similar to what Act444 posted about differences between the lenses as well as specs and such:
Â¤ The 70-200 features a constant aperture of f/4.0 through the entire zoom range, while the 70-300 only retains f/4.0 at 70-103mm which turns into f/4.5 at 104-154mm, f/5.0 at 155-228mm, and then f/5.6 at 229-300mm
Â¤ The 70-300 weighs in at 1050g (37.1 oz) while the 70-200 weighs in at 760g (26.8 oz) making the 70-200 not much, but somewhat easier to carry around and to use while shooting handheld
Â¤ The 70-200 has a length of 172mm and does not extend while zooming or focusing, the 70-300 extends while zooming and measures 143mm when fully retracted and extends by 53.4mm at 300mm
Â¤ The 70-200 measures 76mm in diameter while the 70-300 measures 89mm in diameter (same as the 70-200 f/2.8 L IS II USM)
Â¤ Both lenses share a minimum focusing distance of 1200mm (47.2'') as well as a maximum magnification of .21x
Â¤ The extending portion of the 70-300 is relatively narrow, resulting in it using the same filter-size as the 70-200 which is 67mm, also the filter threads does not rotate on either lenses, making it easy to use circular polarizers and such
Â¤ The 70-300 has the advantage of an extra 100mm at the long end, but the 70-200 still has the advantage of the already mentioned constant aperture of f/4.0 as well as performing better optically, and if paired with an 1.4x extender the 70-200 becomes a f/5.6 98-280mm
Â¤ Both lenses features Ring USM resulting in very fast, quiet and accurate focusing
Â¤ Like all L lenses, both the 70-200 and 70-300 come included with a lens pouch and a lens hood, but something that isn't included is a tripod ring, which is something that all other white canon lenses come included with (except for the non-IS of the 70-200 as well)
So yeah, personally I'd go with the 70-200 f/4.0 L IS USM over the 70-300 f/4.0-5.6 L IS USM, 'cause not only is the 70-200 cheaper and also lighter, but it also performs better optically, and if I ever need more focal length I'll just pair it up with an 1.4x extender, or perhaps even buy the 200-400 f/4.0 L IS USM Extender 1.4x when it's released, though that lens will probably be somewhat expensive.
Of course there are other alternatives, like the non-IS version of the 70-200 f/4.0 which is an incredible lens as well, and the price is just too good to be true. Personally I prefer lenses with IS because of shaky hands, which then also rules out the 70-200 f/2.8 L USM, for me at least.
But those that are real steady when handholding, or that uses tripods most of the time, should definitely consider the non-IS of the 70-200 f/2.8 which is priced about the same as the 70-200 f/4.0 L IS USM if I'm not mistaken.
Then there is of course the bad boy itself, the king of all the Canon 70-200 lenses, the 70-200 f/2.8 L IS USM II, but it's priced almost twice as much as the f/4.0 IS and the non-IS 2.8, so it may not be an option for everybody.
I have also heard good things about the Sigma 70-200 the and Tamron 70-200 so they may also be an option.
My post turned somewhat into an 70-200 orgy even though this thread is about buying the 70-200 f/4.0 L IS USM or the 70-300 f/4.0-5.6 L IS USM so my apologies for that.
To sum it up, both lenses, the 70-200 f/4.0 L IS USM and the 70-300 f/4.0-5.6 L IS USM, are extremely good lenses, and you can't go wrong with them, what ever you choose, you willl without a doubt be a very happy man/woman, but personally I'd choose the 70-200 in a heartbeat, ok maybe not in a heartbeat, but I'd go with the 70-200, there's just something magical about the focal length 70-200 you know?
PS: I just had to mention that as well, there's also the non-L 70-300 lens to, but those that have the L-fever won't probably realize that it even exists ;P