Wildlife is, by definition, wild - you usually can't get all that close.
Unless you stand really still and they just walk right by you, like this little one did the other day while I was shooting Pelicans in flight. He was about 6-7 feet away (as you can see from the angle). This is the @600mm (300 2.8 IS II + 2x III), ISO 6400, 1/500s on my 5DIII, processed with the new DxO 9 PRIME. Killer combo on all fronts (forgive the white balance):
Personally, I'll likely get the 300 II at some point soon. However, while that's partly as a more portable bird/wildlife lens, it's main use will be sports, since my older daughter is now starting to participate in several.
I find it a killer combo with the teleconverters and as you say, it can be used for sports, landscapes, and many other things as well. I have hand held it 99% of the time no matter the light.
To the OP, I find 600mm enough reach for most wildlife, because most of what I shoot is either close enough for 600mm or way too far for an 800mm + 2x. Being able to drop down to 300mm is great for closer subjects as well, and I hear the 300 + extenders/extension tubes also make it a great macro lens for less than 1:1 work. To me, it's versatility and price trumped the other options. I'll happily rent a 600mm for trips and other occasions, though.