It's also worth noting that the ding for all-zero CC balances is a particular specialty at Equifax. I did a series of tests a couple of years ago of what the impact was, for both EQ and TU like your comparison. I found my EQ FICO score went down by 4 points and TU FICO went up by 6, for all zero balances, compared to my usual situation maintaining a $10 balance on one card account. I went through several cycles and found this pattern to be absolutely repeatable. YMMV, of course.
Starting Score: EQ 804 - (April 2009) 