Both are Bristol specialists. Both work with the highest integrity, and both will provide quality work for quality prices. Both have extensive knowledge on Bristols - for example, how to remove the rubber suspension bushes to restore the handling to its design spec performance (on recollection I was told they use a gas axe that produces prodigious amounts of black smoke in the workshop but gets the job done).
For a long time, SLJ was the independent whereas Coleman worked for Bristol Cars. There was friendly rivalry (as I learned with the infamous Gant steering wheel), but both were the top go-to for anything Bristol.
It probably will come down to how far away each is from you.
As for the power train, as others have said, it is Chrysler, meaning volume over precision that can be worked on by any Yank mechanic or even hotrodder. It's not like servicing a Bugatti Veyron where an oil change in California costs US$25,000 (takes 27 hours every 6,000 miles or once a year). See
https://youtu.be/PYpexKP_jTs?feature=shared&t=31
But when it comes to upgrades, like replacing the original Carter carb with something better on the market, begin by educating yourself. The several forums will have members who have been there and can give you their real-life experience. Once well informed you can either select a Chrysler specialist or the two Bristol specialists to do the job (or DIY, it's not that hard).
One of the appealing aspects of a Bristol is that they were hand made by men in a workshop not robots on an assembly line. This means they can be repaired by people with man-sized hands, and the dreaded no-longer-available status of mass production parts is not so much of a concern with Bristols. My 411 was missing the bottom engine cover, so when I was in London, I ordered another from Brian Marelli on Friday. He said it would be available Monday afternoon. Turns out to have been a simple piece of bent aluminium that the factory cut and bent from a template on Monday morning and Tony Crook flew his plane over to collect. With measurements and specs, I could have had my local metal press make it, but I also got a good story out of it for free.