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I handled both of those doubles just a couple of days ago.
I have handled a lot of doubles over the years, I could hunt with either one of them.
In fact, if I was flush with money, I would have bought the Jeffery for my wife as the short bbls would make it easier for her to carry and shoot.

JJ told me a prior owner of the Jeffery had him shorten the barrels.
The Jeffery handles and feel good.

The Watson appears to be made by the Jeffery makers,
[as is my Edwinson Green and Sons 450 No2].

It too is a nice double that handles good.

Almost all doubles made by "Jefferys makers" fit me best of all.
You should go to Enid and get the one that you like the best.

If I got the Watson I would have JJ fit a new Schmidt&Bender 1.1-4 Zenith with the illuminated reticle in a set of low claw mounts. He did that on my 450/400 and it handles great.

Either one of those doubles, with whatever JJ thinks needs to be done, done, would make an excellent double.

I say again you can never go wrong with a British 450/400.