Hi Huw,
I shoot canon and quite often use a 1.4x teleconverter. I mainly use it on these lenses: 70-200 f2.8, 300 f4, 400 f4, 150 f2.8 macro.
With a 1.4x you will lose one stop of light but I still have excellent image quality and autofocus.
You will lose 2 stops of light with a 2x and may notice a difference in sharpness and especially autofocus accuracy and speed. That has been my experience anyway.
Keep in mind I use a crop sensor camera not full frame.
I’d go with the 1.4x.
@Diane_Miller uses both teleconverters on her full frame canon and may have other insights.
I generally keep my 1.4x on the lenses I mentioned all the time for the extra reach.
My Sony 100-400 lens is the best I can afford f4-5.6. This will take the 1.4 and one stop from tele end will make it f/8 so I think the 2x will be too restrictive with 2 stops f/11?
The best thing about TCs is you keep the mfd. For DFs I find the 2x the most useful, on the 100-500 at 1000 mm so I’d guess the 2x would be better unless you can get very close to them. For flight the 1.4x would be better with a little better DOF for easier focus. For a 100-400 the 2x would not be a big penalty. With the Canon 200-800 at 800 it is difficult for flight but at 400 or 500 mm no big issue.
Sony lenses are excellent and I doubt you would see any quality loss. I see slight softness at 1600mm but the sharpening slider in LR protects it nicely.
Huw: I have the Sony 2x for my FE-70-200 f2.8 and FE-f2.8 macro and see zero ill effects BUT bear in mind that even with the TC aboard I still have f5.6 and the AF works reasonably well. OTOH with my A-mount 70-400 f4-5.6 on my A77II the AF is almost totally worthless with the Kenko 2x and barely useful with the Kenko 1.4x. Paired with your FE lens and your 7rV you might expect significantly better results. The Sony FE TCs are the same price so I went for the 2x for the extra reach. I’m even happier with that choice when I bought the 100mm macro because with the 2x aboard I can get 2.8x magnification. I’m not too concerned with the light loss since one can simply bump the ISO and let the good camera and processing software tame any noise. >=))>
There was a time when people shied away from 2x converters due to image sharpness and autofocus capability. I believe that has changed significantly. I shoot Canon RF, and I is difficult to tell a difference in image quality regardless if use 1.5 or 2x. Many bodies will now have several focus points capable of focusing at small apertures.
I’m not familiar with Sony or specifically which body you are using, but you should be able to find that information easily. If the autofocus capability of the body will work with 2x I would go that direction. I’m sure Sony, like Canon, pretty much have the image quality issue resolved.