We have a requirement for upgrading the PHP version (5.3.25) to current stable version which is 5.6.17. So, for this we need to find which approach would be best.
On my experience, we upgraded our PHP version from 5.3.28 to 5.6.6 directly because of server upgrades, and one more reason is you can easily check all your modules faster if there's an error rather than checking it on every version.
What you should keep in mind: