There is no security difference between POST and GET. If you do not want to have the resubmitting problem. You should follow the Redirect-After-Post pattern.
Edit:
For all the guys seeing a difference in terms of security.
- You can sniff either of those via Man in the middle in plain text(while not having https)
- You can resend both requests
- You can invent security tokens for both methods
- The only difference is that POST does not expose information by the URL identifier. But an attacker will always check also sourcecode.
Having POST to insert data in databases etc. is not because of Security. It is because of the widely used REST paradigma. But the REST paradigma is not a MUST while developing a web application. It is like any standard you may follow its guidelines or you leave it alone.
There is btw also a nice post on the exact same topic with the same findings: Is either GET or POST more secure than the other?