L lens ? 70-200mm vs 100-400mm

I like to shoot wild life mostly, (birds and animals). So I shoot outdoors most of the time. I was considering one of these lens. I just have a cheap 100-300 lens now and I do like the reach of it and sometimes I wish it had more.
EF 70-200mm f/2.8L USM Autofocus Lens with 1.4 or 2.0x teleconverter so I could have the 2.8 for low light when needed but would give up my long zoom or get the
EF 100-400mm f/4.5-5.6L IS USM Autofocus Lens Need opinions on which would suit me best. I think they are close in price so that probably wouldn't be an issue.

For shooting birds 70-200 is simply no good. Stacking 1.4x, you'll find it too short still, unless you can set up stealth methods to get closer to unsuspecting birds. With 2x you lose too much IQ so you won't be happy with the results. So I'd say go with 100-400.

Another alternative that would give you even more reach is the "Bigma" (Sigma 50-500). A lot of people seem to appreciate that lens as well.

Why not go for a prime lens. A lot lighter, better bokh, faster aperture.

One thing you might consider as I have...
For the price of the 70-200mm f2.8, you can probably pick up a prime 200mm f2.8 EF lens, which will have better picture quality with a 2x teleconverter, and a second digital camera body.
Just keep the 100-300 for whatever...

Most definitely the 100-400 over the 70-200 for your wildlife requirements. This is a great lens for this. I would not recommend a 400 prime unless you were shooting long bird shots. I would bet only 25% of my shots with this lens are at 400 with many at 150 and up. You could add a long prime at a later date you find you do use the lens at full zoom a lot. I have used a 1.4X TC with my 100-400 with good results, you lose AF but can retain it by taping 3 of the contacts though the focus then hunts a lot and is not very fast.

for wildlife and birds the 70-200 will not cut it, not even with a TC, especailly not the 2x because it has hoorible image quality. the 100-400 on the other hand is a great wildlife lens.

Thanks alot guys for the info. Looks like the 100-400 is that way to go for me