I'm currently running TFS 2013 on one Windows Server 2012 box and TFS Build 2012 Update 4 on another box. My question is if I upgrade my TFS Build Server box to utilize TFS Build 2015, will I need to upgrade my TFS 2013 Server as well?
Also, what about the opposite? Can I upgrade my TFS 2013 server to TFS 2015 and still use my existing TFS Build 2012 Server which is using web deploy to build and publish to various other servers on our network?
Yes, TFS Build 2015 and Build vNext require your main TFS server to be at least 2015.
The other way around, TFS 2015 can talk to Team Build 2010, 2012, 2013 as well as the new 2015 build agents of course, as long as they're updated to their latest service pack and update version.
Upgrading your TFS 2012 build server would not be too hard either, depending on the amount of customizations made to the build workflows.