Tough to say without knowing what you'd be shooting.
Keep in mind, for the 100-400, if you use an extender you lose autofocus. For the 300 f/4, you'll lose AF with the 2x extender, but still have it with the 1.4 extender.
Obviously the zoom gives you more flexibility, and while I've never used either lens, you're probably correct in saying that the 300 f/4 has better IQ.
I personally wouldn't go with the 100-400, because it has a push-pull zoom, and to me that's way awkward and is essentially a dust vacuum.
Focusing shouldn't be an issue. That's what you have AF. If you're shooting at far away subjects, you'll be focusing towards infinity anyways, which doesn't make too much of a difference on focusing.
I'd be able to give you better advice if you let me know what your target subjects are.
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