If you plan to upgrade, you will need to apply the upgrade to the old location before moving; you cannot run both 7.1b4 and 7.0.2 as 7.1 has additional table formatting that has to be applied which shouldn't work with 7.0 nicely.
You should upgrade your current install, then move; or move then upgrade (and delete your old files).
Again, running 2 separate installs with the same database is not recommended, regardless of if they are different versions or not.
