Hopcar, Your "Sea Dog" is a type Hinz says is good (he calls it a "bridled grabber"), it seems to put an even load on the link that sits into it, the load is in the pull direction of the snubber line. The second "claw" or "grab hook" type you show, which I have, is "not recommended" by Hinz,it sits transversely across a link against the link above, the upward pull is not aligned with the chain.Lots of people use them.
With the chosen device in place and its line cleated, you let go some chain, the load shifts to the snubber line, off the chain which becomes slack, unloading the windlass. The gadget can, but rarely comes loose in the process. With load on it, it can`t come loose.
Your "Sea Dog" use 2 lines, the claw uses one. Defender`s "Captain Hook" Chain Snubber is pictured with one line, Hinz calls this a "devil`s claw"and rates it good. Check it online, in my older catalog, it`s item 000141(to5/16") or 000465(to1/2"),to me it looks better than the one Hinz shows with bent over metal prongs. Hinz has a 3rd one, a "Devil`s Claw Hook" he rates excellent.
I have rubber mooring snubber in the line to my claw. I will be interested what you think.
Hinz references: p117,3rd edn,"Complete Book of Anchoring and Mooring"(as recommended by Marin).