1: your lens needs to outresolve the sensor at the longest focal range. If it doesn't you won't gain anything.
2: you lose f-stops if you put on the TC. (The light gets distributed on an area 2 or 4 times as big, leading to 1 or 2 f-stops loss of light density on the sensor.)
3: Your lens needs to be wide enough to still reach f/5.6 for autofocus. (Autofocus also gets slower with extender due to less light on the focusing mechanism. Low light performance is worse.)
4: you may want to stop down further to f/8 because that usually improves the image quality and resolution.
5: you may need a tripod because 800 mm focal length are hard to hand-hold.
Since you write about the 100-400mm lens on a 22MP FF-body, i assume that it would go well with the 1.4x extender since then the resolution matches a crop body with 18MP without extender. The 2x extender would most likely result in blurred images which don't provide more detail. Also the overall image quality reduces severely with 2x extenders. It's not just resolution but also contrast CA vignetting distortion etc.
What you could try is to use MF and shoot at F/8 without extender and if you can work with that, go for the 1.4x extender (or better yet get a used crop body, which equals to about 1.5x extension but with working AF and no f-stop loss).
EDIT: I may have misunderstood you. Decreasing the sensor size is always better than a TC. So a crop body with all other things equal will always be better. Unfortunately you also have to consider price, weight, different performance of different bodies, different noise characteristics etc... I for myself use a crop body + TC.