Canon EF 100-400mm f/4.5-5.6L IS vs EF 70-200mm f/2.8L IS II (with 2x converter), which one is better?

Tony Northrup on YouTube compares the Canon EF 100-400mm f/4.5-5.6L IS USM with the Canon EF 70-200mm f/2.8L IS II USM (mounted on a Canon 2x teleconverter).

Which is better? If you get the Canon EF 70-200 f/2.8 L IS II lens and add the Canon 2X III teleconverter, you’ll be able to use the 70-200 at f/2.8 when you need to and two stops more light (and background blur) in that range than you can with the 100-400 II. When you need the extra reach, you can add the teleconverter and jump to 140-400mm f/5.6. The total cost is pretty similar, so which is better? Will the teleconverter make the 70-200 noticeably less sharp at 400mm?

Watch the video review to learn how the two lenses compare.