The advantage of the 100-400 over the 200-600 is size (smaller diameter and shorter especially if not zoomed out) and weight (almost two pounds). I have the 100-400 and on the occasions I need extra reach I switch to JPEG and activate Sony's CIZ (Clear Image Zoom), which I find gives excellent results at 1.4 and is still good at 2.0. The 100-400 is easy to carry and hand hold, so I'm very pleased with this approach, especially since using the CIZ "teleconverter" entails no loss of light and does not require mounting/dismounting the lens in the field.

Tamron does have a 150-500 which has had good reviews and, if I'm not mistaken, falls between the other two in heft.

Here are the results from an exceptionally thorough comparison of the two Sony lenses by Timothy Mayo:

Conclusion

Both lenses are exceptionally good and although only the 100-400 is badged as a G Master lens, the 200-600 G would certainly not bring any shame to the GM label if Sony had decided to use it.

If you are shooting wildlife then most likely you are going to want as much reach as possible and although you can add the 1.4x teleconverter to take the 100-400 to 560mm / f/8, you will see a noticeable drop in image quality especially compared to the 200-600 at 600mm f/6.3. You’ll also now be shooting at f/8 and will need to crank the ISO a little higher.

If you often shoot using a gimbal then you’ll also find that the 200-600 balances much better since the barrel does not extend when you zoom and throw the balance off. With the 100-400 on a gimbal you’ll either need to fix the zoom and then balance it, or put up with the lens being off balance.

The smooth internal zoom of the 200-600 which features a very short zoom throw also helps to keep your subject in the frame and I find it much quicker to use compared to the 100-400. When you zoom with the 100-400 the weight also changes which affects the balance, and if you are shooting skywards there is also a lot more resistance.

Shooting from a hide with an internal zoom is also beneficial since there is no movement to scare away your subject, whilst zooming in and out with the 100-400 can be risky if your subject doesn’t know that you are there or is very nervous.

The 100-400 is the lightest lens of the two weighing in at 1596g (with tripod foot and hood attached). Without extending the zoom it measures 205mm in length, extending the zoom to 400mm takes it to 285mm. The lens has a maximum diameter of 93.9mm. Adding the 1.4x teleconverter will add an additional 169g in weight and also adds 16mm in length. Without a doubt if you are travelling a lot then this is the lens you will want in your backpack.

The 200-600 weighs in at 2397g (with tripod foot and hood attached), making it a good 800g heavier than the 100-400. It measures 318mm in length with a maximum diameter of 111.5mm. If you are used to shooting with the 100-400 or a lighter lens then you will most definitely feel the weight of the 200-600, especially if you are handholding. But if you are used to the weight of a big prime lens with an SLR camera attached then it will probably feel like a feather to you.

With a minimum focus distance of only 0.98m (3.22 ft) the 100-400 is the best choice for close-up photography, since the 200-600 requires 2.4m (7.88 ft) to autofocus correctly. So if you enjoy shooting butterflies, dragonflies and other bugs then the 100-400 is probably the best lens for you.

The 100-400 does handle chromatic aberration a lot better than the 200-600, it shows no signs of CA in either the center of the frame or towards the edges. The 200-600 shows signs of CA both in the center of the frame and towards the edges where it becomes more pronounced. With lens corrections turned on CA is minimized but still visible, so you may need to apply further CA removal in post if shooting subjects with high contrast. Thankfully I’ve not spotted any CA in the real world images that I’ve shot with the 200-600 so far, but I will certainly be keeping an eye out for this.

If money was no object I would own both of these lenses since they both have their own unique qualities and both are capable of capturing some amazing images. For me personally I now prefer shooting with the 200-600 mainly for the extra reach and internal zooming. My shoulder muscles are just going to have to grow to handle the extra weight!

Whichever lens you choose I don’t think you are going to be disappointed one bit.

https://www.alphashooters.com/compare/sony-fe-200-600-vs-fe-100-400-gm/

Another thoughtful perspective:

If you are looking [for] a bird lens or wildlife strictly then the 200-600 is superior. If your looking for a jack of all trades birding lens with the 1.4 ext that is smaller, packable as well as a macro, landscape, butterfly and general use telephoto the 100-400 is preferable. For the most part the 100-400 makes up for less [focal] length by being useful in a lot of ways. It's more expensive, but if I had to carry one on a hike there would be no choice 100-400, unless I was shooting birds only and it was a short hike. 200-600

https://www.dpreview.com/forums/thread/4421840