This is what I found on the Apple Support Communities:
The Verizon problem isn't the phone. The problem with Verizon is they will not allow phones on their network that were not purchased for use on their network. This is entirely a Verizon issue.
Sprint recently changed their policy (as part of an industry-wide agreement), and they will unlock a phone that has met its commitments for use on any GSM network. Unfortunately, a lot of Sprint CSRs haven't read the memo, so you may have some difficulty getting it unlocked. But if you persevere you can probably make it happen.
For the 5S and Sprint the situation is the same. However, all Verizon 5 series and 6 series phones are unlocked out of the box, even before you meet your commitment.