I'm a budding wildlife photographer, so take this for what it's worth.
I have both the 70-200 f/4 and the 300 f/4D, along with the TC14-II teleconverter, and I use the 300+TC14 for wildlife shots, along with a monopod. I plan to replace with the new 300 f/4 PF VR once available due to the significant weight and size reduction and the VR. I think the best answer to your question depends heavily on a couple things:
1. What is your definition of "wildlife?"
2. How do you prefer to setup for wildlife photos ( sitting in blind vs. sneak as close as possible)?
3. Will it be a dedicated wildlife lens or serve double duty?
If your wildlife interest is large mammals like deer, elk, bear, etc. then the 70-200 can work, if you accept you'll be doing a lot of cropping and/or you're using it on a DX body. The "naked" 300 will be much better for frame filling shots as long as you're able to get within 75 yds or so of your subject. The 300 with 1.4X teleconverter gives you the most ideal reach, but since you have max aperture of f/5.6 with the tele attached, it's not the best in low light, and you will be taking a lot of ultra high ISO shots, as the best times for wildlife sightings are early morning & late afternoon. For that reason, I wouldn't personally go above the 1.4X tele, as you're already very compromised on light transmission as-is.
If you're mostly into bird photography or small animals that don't allow you to get close, IMO, the 70-200 simply doesn't have enough reach most of the time, and even the 300 is barely adequate at best. The 300 + tele is o.k. as long as you're able to get fairly close.
If you typically like to take wildlife photos from a blind, you can get away with less focal length than if you prefer to try to "sneak up" on critters or just snap photos as opportunity arises. If you do the latter, I would definitely wait and get the new 300 f/4 with VR so you will be carrying a much lighter, more compact rig, with less dependence on a tripod. Even so, I like to take a telescoping monopod with me when I go looking for wildlife, especially once light levels get lower.
If your "wildlife" interest is mostly large mammals and you also want to use your lens for, say, portraits, the 70-200 is more flexible, and you can attach a teleconverter for wildlife as needed.