As far as throat erosion stainless tends to do better because it absorbs heat slower , as well as releasing it, and suffers less fatigue during expansion at moderate temperatures. Even though it is not by much.
4140 is capable of much higher strength and hardness when tempered, but experiences cracks throughout the surface of the throat as the rapid expansion and contraction during shot strings and begings to erode quickly. As well as its tendancy to react with the very corosive properties of modern powder under high heat and pressure. This is why they are so often chrome lined.
Although these differences are minor and present it would not keep me from buying a carbon steel barrel.
Lilja touches on this in their FAQ section
Lilja Precision Rifle Barrels - FAQ
Rifle shooter mag also has s good write up on it.
All About Barrels
Otter i hope you find this useful.