I have MkII versions of the 1.4x and 2x. Any extender will reduce IQ - how significantly depends on the lens with which it's used. In your case, you list 70-200 f4L IS, 70-200 f2.8L IS II, EF 300 f4L IS, EF 400 5.6L. The 70-200mm f/2.8L IS II takes extenders very well, the 70-200mm f/4L IS will take a 1.4x ok, suffers with a 2x (and no AF due to f/8), the 300/4 does ok with a 1.4x (IQ will be a bit less than the 400/5.6 and 100-400 @ 400). The 400/5.6 also does ok with a 1.4x, not so good with a 2x, but any extender on the 400/5.6 means you lose AF.
In general, the TCs work best with the supertele lenses (300/2.8, 400/2.8, 500/4, etc.). With zooms and lesser primes, there's a bigger IQ hit.
Also, the 1.4x extender slows AF by 50%, the 2x by 75% (by design). That's fine for static subjects, ok for moving ones with a fast-focusing lens like the 70-200 II, can be a problem with moving subjects and slower focusing lenses (the 300/4 isn't 'slow' but it's not as fast as the others).
Do you mind manual focus or Live View? I ask because you already have a 400/5.6 prime - a 2x on your 70-200 II gets you to 400/5.6, and a 1.4x on your 300/4 gets you to 420/5.6, so while both combos do give you a lens with IS, it's no longer (or not significantly longer) than your 400mm prime. Adding the 1.4x to the 400/5.6 prime, as stated, means 560mm f/8 and no phase AF (unless using it on a 1-series body prior to the 1D X), although Live View AF works, albeit slowly.
I tested the 100-400mm with the 1.4x extender, and was happier with the shot at 400mm cropped to the 560mm FoV over the shot with the extender. I've taken some shots with the 100-400mm and the 2x - turned out ok (not great), but focusing was a pain at f/11.
I do find the extenders useful occasionally, mostly when I'm going out to shoot with my 70-200 II primarily (outing with kids), but bring the 2x just in case. The other situation in which I find the extenders useful is that with the 70-200 II, the combo is weather sealed, which the 100-400mm is not (nor are the 300/4 or 400/5.6). I'm actually considering moving from the 2x II to the 2x III (and selling the 1.4x, which I just don't use much at all).
FWIW, here are a some examples - the first two on the 7D where I was using the extender + 70-200 II in drizzle/rain (the 1.4x shot was before I had the 2x), the third was bringing the 2x along on a trip with the kids where I brought the 5DII and 70-200 II. Clicking them then View All Sizes in the upper right will get you to a 1600 pixel version if you want to check sharpness.
EOS 7D, EF 70-200mm f/2.8L
II IS USM + EF 1.4x II Extender @ 280mm, 1/2000 s, f/6.3, ISO 3200
EOS 7D, EF 70-200mm f/2.8L
II IS USM + EF 2x II Extender @ 400mm, 1/160 s, f/5.6, ISO 3200
EOS 5D Mark II, EF 70-200mm f/2.8L
II IS USM + EF 2x II Extender @ 260mm, 1/250 s, f/5.6, ISO 400