I would have never guessed this, but the free Kindle version of the TNIV has been downloaded more than the free Kindle version of the ESV.
Go here to see the results
TNIV is 7th while the ESV is 20th. (There is actually another version in between, "God's Word" Translation). I think it is impressive that all three are in the top 20 (the price tag may help that.)
I have both TNIV and ESV on my iPod touch.