If you are not in reach-limited situations, then there is no advantage image-wise in using an extender or using a crop with smaller pixels. FF without an extender will always give better results. But, if you are in a reach-limited situation, then it may be better to use an extender and a crop camera.
The usefulness of extenders depends on the lens and body. To assess the merits for an up and coming bird-watching trip, I spent yesterday recalibrating with Focal my 5DIII and 7DII with my 100-400mm II and 300mm f/2.8 II with 1.4 and 2xTCs, I spent some time staring at iso-12233 charts snapped with the recalibrated lenses.
Conclusions:
1. 100-400mm II on the 7DII does out resolve the 100-400mm II on the 5DIII, with some loss of contrast.
2. 100-400mm II on the 7DII is very similar to the 100-400mm II + 1.4xTC III on the 5DIII in both contrast and resolution.
3. 100-400mm II + 1.4x TC on the 7DII does out resolve the 100-400mm II 1.4x TC on the 5DIII, with loss of contrast.
The situation is different for the 300mm f/2.8 II. On the 5DIII, the addition of 1.4 and 2xTC IIIs leads to a progressive increase in resolution, but the 7DII doesn’t work well with the 2xTC (as I have found in the past from experience), and is best at 420mm with the 1.4xTC.
So, I’ll be packing both bodies, the 1.4x TC and the 100-400mm II to take with me; the 7DII for distant bird watching and the 5DIII for closer work in darker situations. For mild hiking at home, the 5DIII with 300mm f/2.8 plus 2xTC is still my preferred combination, but I am increasingly grabbing the 7DII + 100-400mm II.
Edit, here is the summary of shots of the centre of the chart that led to the conclusions - self-explanatory.
