I would polish the new rifles chamber as it looks like it has a sharp edge or burr. If it is undersized you can use some valve grinding compound on 0000 steel wool on a solid cleaning rod chucked in a drill.

If the chamber is within specifications then use Flitz on the steel wool only. Don't hit the shoulder area with grinding compound as it could create a head space issue. I would be tempted to re-ream both rifles to match as I don't like having to segregate brass.

"When you disarm the people, you commence to offend them and show that you distrust them either through cowardice or lack of confidence, and both of these opinions generate hatred." Niccolo Machiavelli