When having a custom rifle built would it be better to -- Have your custom action sent to the barrel maker for fitting, or, have your barrel sent to the action manufacturer for installation?
Or put another way who generally is better suited equipment wise for the best job? Barrel makers or action manufacturers?

Depending on what action it is, I would send it to a good custom gunsmith and have him barrel it. The downside is the time involved but you would end up with a more accurate rifle as far as I am conserned. www.benchrest.com has a lot of very good gunsmiths listed.
If you do decide to go that way, email me and while not recomending a gunsmith, I will let you know a few to stay away from.

There's several extremely good folks right here that frequent this forum that can do a superb job of attaching a barrel and chambering it to your action. I don't do it for others normally but for example Jim Kobe is a superb craftsman and there are many others too.

With any luck you'll get a PM or two.

It's not at all uncommon however to send an action to a barrel maker to have it fitted as well.