Carbon black being a 3rd party ink or just the Epson black?
Either way, I’d suggest ABW for a number of reasons: Less colors of ink used, more archival, control over color toning, no issues with metameric errors, and with Epson Print Layout, soft proofing of this with your own images.
Author “Color Management for Photographers" & "Photoshop CC Color Management" (pluralsight.com)”
Carbon Black, a.k.a. Black Enhance Overcoat is a particular setting in the Epson driver for the P700/P900 models that is available for high gloss papers. It can be used on these papers in either non-ABW or ABW driver modes. All discussed in my article. The best way for you to decide which mode to use for B&W printing is to select one or two of your favorite B&W files and print them using several optional settings with and without ABW and seeing which you like best in terms of controls and results.
Mark D Segal Author: "Scanning Workflows with SilverFast 8, SilverFast HDR, Adobe Photoshop Lightroom and Adobe Photoshop". Please check the PhotoPXL Store for availability.