Which is better for wildlife and sports on a Canon Rebel T6: EF 200mm f/2.8L II or EF-S 18-200mm IS?

First, I would like to make some corrections to your post :

Canon EF-S 18-200mm f/3.5-5.6 IS:

• Zoomable (I will probably use it at 200mm 80% of the time)
• Max 200mm effective.
• f/5.6 at 200 mm.

Even if the lens is an "EF-S" lens (meaning it is made for an APS-C sensor), you still need to apply the 1.6x crop factor to get the 35mm focal length equivalent. 200mm at f/5.6 will yield a 320mm at f/5.6 on a 1.6x crop sensor. More info : Does my crop sensor camera actually turn my lenses into a longer focal length?

• Image stabilization.
• About $700.

$700 for this lens seems a little too much : where I live, you can a new one for about $500

Now, regarding the need for stabilisation, keep in mind that IS only helps to prevent blurring from camera/photographer movements ("camera shaking").

I would probably use it 80% of the time at 200mm taking pictures of animals (including birds) at wide apertures for fast shutter speeds (with enough light to use low ISOs in most cases).[...]

For that, stabilisation probably won't help you : you will need fast shutter speed to capture the animal movement (probably 1/500 or faster). The rule of thumb to prevent camera shaking is to shot faster that 1/(focal lenght). At 320mm, you will probably be fine. Related :

• How can I determine the minimum shutter speed to avoid blur from camera shake?

• How can I use image stabilization to make a moving subject clear?

[...] Apart from that, I would probably take some portraits with good light [...]

Again, no need for stabilisation. On a sunny day, the rule of thumb to get a good exposition (Wikipedia) is to use the following settings : aperture of f/16, shutter speed of 1/ISO. So, as you want probably to use a larger aperture for a portrait (f/5.6 or lower), you will need to use a faster shutter speed than 1/250, even if it gets a little cloudy.

[...] some sports photos in medium light conditions and some animals in low light conditions (very uncommon).

The shutter speed required to get sharp image of "sports" depends on the kind of sport. For football, 1/500 seems to be a minimum to freeze the movement, for chess, it is probably a lot less. I often take picture if my wife playing indoor handball with a 70-200 f/2.8, and I need at least 800 to 1600 ISO to get a correct shutter speed (1/500 or 1/1000) at f/2.8.

So the real challenge is animals in low light conditions... But with a regular Canon crop body where 1600 or 3200 ISO seems to be the upper limit regarding image quality, almost no lens will help you, and the price tag for those qho might is not in the same category as the lenses you take into consideration here. Using a tripod might help if the animal isn't moving much, but what you really want at this point is the larger aperture you can get and a high-end camera capable of high ISO (probably full-frame) : be ready to pay thousand of dollars !

Now regarding lens performance, a lens with a fixed focal length is always better than any other zoom with a similar price : you will get a lot less distortion, chromatic aberration,... It is also studier (less moving parts). On the other side, the higher the focal range of a zoom, the lesser the image quality. So when shooting at 200mm, a 200mm lens (fixed focal lenght) is probably the best choice. To see for yourself, you can look at this comparison from The Digital Picture (18-200 vs 200mm at f/5.6 with the same camera).

So to conclude, at your place I would probably pick the 200mm f/2.8 L or the 70-200 f/4 L (and disregard the stabilisation)... but you are the one having to examine all issues and only you knows how you want to use your lenses.

Here are some other related questions, so can can get more knowledge before choosing your futur lens :

• Should I keep Image Stabilization (IS) off when I do not actually need it?

• What reduces blur from camera movement more: large aperture or image stabilisation?

• Focus problem vs. motion blur vs. camera shake - how to tell the difference?

• How can I take crisp sharp shots without an expensive lens?

• How can I hold my camera steady?