99% of my client base would rather have a newly built gun on oversized and properly fitted parts with the Chambers Custom name on the frame than a rebuilt brand XXXXXX. It took me a long time to understand why guys continue to build on other brands, but I do understand. Just like most of them understand why guys like myself get an 07 so we can have frames made to our specifications with our names on them.
There are, in my opinion, places in the market for both options. And there are, again in my opinion, people who can do both well. It really boils down to what the client desires. Early in my career I spent enough time rebuilding factory guns to realize the time vs. money ratio simply doesn't add up for me or my clients. The exception to this rule for me is sentimental value of the base gun. That and the fact that no one has yet been able to prove to me that a Colt built into a custom is more valuable than a properly built gun by a quality smith.
So I say to you, if you like rebuilds, awesome! Find a smith that is capable and willing to do the build for you. If you like "new guns" then awesome! Pick a builder from a relatively small pool of men who can take oversized parts and fashion them into a properly functioning pistol of your choosing.
And at the end of the day remember to smile, because either way you'll have a 1911 in your hands, the way God intended man to live.