First, login with same Live account won't work because they are created as different local account on those computers. And by login through live account, the old "if no access, try send clear text username and password" fallback won't work because the password is not known by both PC.
Now create account on both machine that has same username and password, and use that account to run the debugger and IDE.
Now check this article for other things to check (it's written for VS2010, but things still hold true for VS2013 as well)
EDIT: The article doesn't mention the setting in Local Security Policy that matters. "Network access: Sharing and security model for local accounts" should be set to "Classic" instead of "Guest Only", or your machine will try to authenticate to the remote debugger as guest,