I had to choose between (CANON 70-200/2.8 L IS II with CANON 1.4X II extender) or an (EF 70-300mm f/4-5/6L IS USM) for wildlife photography, what would you recommend? Would the better image quality from the first lens be comprimised by using a teleconverter so that I might as well use the second?
This is an old and endless debate, so you're not going to get a single answer. My recommendation is to do some searches, gather all the info you can, and decide which works best for you. There are some good thread at dpreview and Canon Rumors on this.
I'm going to muddy up the decision even more and toss the 100-400L into the mix. General take is, if you do a lot of shooting in low light get the 70-200, if you mostly just shoot wildlife choose between the 70-300L and the 100-400L. But even that is debateable. Some don't mind lugging the extra weight of the 70-200 and dealing with extenders. I think the IQ is close enough with the 1.4X to call it equal. But there are plenty of people on the internet with test charts to argue otherwise.
The 70-300 vs 100-400 discussion is equally as undecided. 300 has a bit better IQ, 400 has extra reach. Decisions, decisions...
I'm with Skirball on this one. Either one is not the optimum choice for wildlife photography - mostly due to lack of reach. But to specifically answer your question I'd unhesitatingly choose the 70-200 f/2.8L IS II with the 1.4X . The reason is not because the 70-300mm is a bad lens (it's not) but because of the versatility in my recommend choice.
The 70-200 II is by far the best lens in its class. It is favored by all including wedding photographers for portrait work. AF is lightning quick, even when you put a 1.4X or a 2X on it. With the 1.4X, most will not be able to tell any degradation in IQ (image quality). IQ is still excellent with the 2X. I have a 70-200mm f/4L IS and a 1.4X II TC and I'm considering getting the f/2.8L when I get more into wedding photography work. I do not use the 70-200mm for wildlife photography at all. I use a 400mm f/5.6L but would not hesitate to use a 100-400mm zoom.
You can't put a Canon extender on the 70-300mm I believe unless you lock (tape it down, there's no lock lever) the FL to near 300mm range. This makes the 70-300mm inadequate for wildlife reach.
My solution, at least for now, is to use a 70-200 f/2.8 non IS for sports and a 300 f/4 for wildlife with a 7D. It's an economical solution with good image quality. The 70-200 also doubles for events with my 5DII.
I can add a 1.4x (or 2X with live view or manual focusing) to the 300 if I absolutely need to.
I have used the 400 f/5.6 but found the long minimum focusing distance an impediment.
If the wildlife is really in the wild vs a zoo you'll need longer than those so the Canon 100-400 L IS would be a good choice or the Sigma 50-500 OS but that's not really a hand hold / carry for hours while hiking kind of lens. From what I've read the 70-300 L is a great lens & I'd own it if I didn't have the 28-300 L because it meets MY requirements more than the 70-200 f2.8 series of lenses BUT many prefer them to what I shoot thanks to differing interests. ALL are good lenses so it's more important to think which fields of photography interest you the most & what lens would get used the most by you. The faster 70-200's or a longer lens.