I suspect even among the best gunsmiths and barrel makers there can be some debate, but FWIW here is what Dan Lilja says about it:
Q. What are the differences between chrome-moly barrels and stainless steel barrels?
"We buy our steels directly from the steel mills. Our steel is made to our specifications as far as chemistry and heat treatments are concerned. Our chrome-moly is a modified 4140 type steel and the stainless steel is type 416 with a few extra steps and tests in its manufacture. We have used steel of both types from several different mills and have settled on what we feel is the best available.
The primary difference between the two types, as far as rifle barrels are concerned, is that chrome-moly can be blued and stainless steel cannot be using conventional methods. Rifle barrels made from stainless steel will last longer, as related to throat erosion, than chrome-moly. Stainless steel resists heat erosion better. Also we can get a slightly better internal finish when lapping with stainless steel.
Approximately 90% of the barrels we manufacture are made from stainless steel. In our experience, most of the chrome-moly barrels we make go on high-grade custom hunting rifles that are going to have a nice custom made wood stock. And some shooters insist on having a blued barrel.
An exception to the above is the large number of 50BMG barrels we make from chrome-moly. Our recommendation for steel choice with 50BMG barrels depends on the bullet type the shooter intends to use. If you are going to use conventional jacked bullets, such as the Hornady or ball ammunition, then the stainless steel barrels will probably last longer and foul less. But if your choice is one of the custom made lathe-turned bullets made from brass, bronze, copper, or even steel, then the chrome-moly barrels will probably last longer and give better accuracy. Please see our comments on moly coating and these types of bullets. If you plan to shoot both types of bullets then the chrome-moly barrels are a better choice."
This Q/A is from right here:
Lilja Precision Rifle Barrels - FAQ
Hope this helps..