Both the 70-200mm f/2.8L (which I will refer to as the f/2.8L) and the 70-200mm f/4L IS (which I will refer to as the f/4L IS) are excellent lenses. The fact that the f/4L IS has slightly better IQ should not be a consideration because I doubt that you will ever notice the difference between these two lenses in real life shooting.I will compare the f/2.8L (non-IS) lens with the f/4L IS since these two lenses are very close in price and differ mainly in the following three considerations.The extra stop of the f/2.8 along with the shorter depth of field this f/stop allowsThe difference in weight.The IS capability of the f/4L IS.APERTUREThe f/2.8 aperture will allow you one stop faster shutter speed which may or may not make a difference in shooting. It will also allow you a slightly narrower DOF which may allow you to isolate specific subjects but, which is also has a fairly steep learning curve.As an example, the total depth of field when shooting at 10 feet with a 200mm focal length at f/2.8 is .96 inches. That is a pretty slim margin but, even at 20 feet, the DOF is fairly narrow: less than four inches. That might be difficult, at least at the start, to work with.You CAN use a 2X TC on an f/2.8L lens and cannot use one with an f/4L IS on a 1.6x camera and retain autofocus. However, IMO and in my experience, the f/2.8L + 2X TC is not a good option for many photo situations. The A/F and IQ are degraded for too much for my taste in any type of shooting.In low light levels, the extra stop of the f/2.8L might not be enough to allow a shutter speed capable of stopping action. However, IMO, in those light levels, an f/2 prime would be the way to go.In decent light levels, f/4 is plenty sufficient. In fact, shooting at f/2.8 is good for specific shots when you want to isolate a subject. Using ISO 400 (which a Canon DSLR has no problems with) your daylight shutter speed would be in the area of 1/6,400 second which will stop virtually any action. However, I suspect, that except for isolating subjects, you may want to shoot at around f/8 to get a wider depth of field. That would give you a shutter speed of 1/1,600 second with either lens.WEIGHTThe difference in weight may be a critical concern. The f/2.8L weighs over a pound more than the f/4L IS (2.8 lbs vs. 1.7 lbs). This can be a major factor when carrying the lens all day or when hand holding this lens. It may not be as much of a factor when shooting sports because photographers often will use a monopod when shooting sports. However, I find that 200mm is on the short side for much sports photography and will use the 70-200mm lens as an adjunct to a 300mm or 400mm lens which I will have on a monopod or tripod. I will use the 70-200mm on a strap when I need a wider view and will normally hand hold this lens.NOTE: Professional sports photographers seldom rely on a 70-200mm lens as their main lens. They will often shoot with a 300mm or 400mm lens on a monopod and simply use the 70-200mm lens hand-held when they need a wider angle of view. See this series of UTube videos by Scott Sewell for a great explanation of the uses of lenses in shooting sports. BTW: Scott uses a 70-200mm f/2.8 IS lens as his shorter telephoto glass.
The extra pound or so of the f/2.8 really makes a difference when carrying two lenses and two cameras for a day of shooting and also makes a difference hand holding at the end of the day. I can carry an f/4L IS lens AND AN ADDITIONAL 1.6x CAMERA for the weight of the f/2.8L lens alone.
The f/4L IS lens is easier for me to hand-hold at the end of a long day of shooting because it is lighter and smaller than the f/2.8L lens.IS CAPABILITY (hand holding)I can hand hold my f/4L IS lens in lower light levels than I can, an f/2.8L lens. At 200mm, I can expect virtually 100% sharp images at 1/60 second using f/4 and if I shoot at 1/30 second, I can still get a fairly decent percentage of sharp shots. I could never get 100% hand held sharp shots using 1/120 second at f/2.8 and I could get NO sharp shots hand holding the f/2.8 at 1/60 second.Much is said about IS not stopping action, however if you cannot hand hold a sharp overall image, it doesn’t make any difference.There are many moving or sports subjects which can be captured at slower shutter speeds. Shooting at the peak of the action is one method. There are also many times you can get sports or other action related shots when the subjects are not moving at all. Two of the greatest sports images of all time, Lou Gehrig’s farewell speech and Babe Ruth’s retirement were not moving.Additionally, an image that is sharp overall except for the blur of a player is often an effective way to show motion and an image that is fuzzy throughout due to camera shake is pretty well useless.
The Mode-2 of the f/4L IS lens allows panning to achieve a sharp subject with a very blurred background.MY SELECTIONI do not shoot sports exclusively and I want a lens which I can use in virtually 100% of my shooting. Having a lens that I would leave at home because I consider it too heavy to carry is not an option for me. I believe that I am not alone in this choice because I have read multiple posts in which photographers are stating that they are leaving their f/2.8L lenses at home when traveling. I have never read a post like that about the f/4L IS lens and I have never left the lens at home when I took a trip. Like the AMEX commercial used to say; “Don’t leave home without it!”The combination of the 17-55mm f/2.8 IS and my f4L IS lenses on two 1.6x cameras is the best camera/lens combo I have used in 50 years of active photography