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:
PHP maintainers upload list of incompatible changes of every release. Here are the documents you may want to read:
If you have regression tests, you're the lucky man; if you don't, i strongly recommend test every change in virtual environment before real environment update on main server. If you're brave enough, you can try to setup vagrant - this will allow developers to easily share their environment and to reproduce server state as it should be after upgrade to 5.6.
I also wouldn't recommend partial upgrades, i think it's better to target for 5.6 at the first (and only) migration step.