Canon EF 200mm f/2.8L II USM or Canon EF-S 18-200mm f/3.5-5.6 IS?

I need a recommendation. I want to buy a telephoto lens and I don’t know a lot about photography. I am looking at these 2 options:

Canon EF 200mm f/2.8L II USM:

  • Fixed lens.
  • Fast (f/2.8).
  • Effective 320mm on my APS-C (Rebel T6).
  • No image stabilization.
  • About $ 700.

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.
  • Image stabilization.
  • About $ 700.

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). Apart from that, I would probably take some portraits with good light, some sports photos in medium light conditions and some animals in low light conditions (very uncommon). What I want to know is what is better for my case? The image stabilization or wide aperture? I don’t think of fixed focal range as an important disadvantage but I’m not sure. What do you think?

I want to also say that the Canon EF 70-200mm f/2.8L IS II USM or similar is probably the best fit for my needs but it is too expensive. I’m thinking of something between $ 600 and $ 800. The same for Canon EF 70-200mm f/4L is II USM.