There are several misconceptions about GET and POST in HTTP. There is one primary difference, GET must be idempotent while POST does not have to be. What this means is that GETs cause no side effects, i.e I can send a GET to a web application as many times as I want to (think hitting Ctrl+R or F5 many times) and the requests will be 'safe'
I cannot do that with POST, a POST may change data on the server. For example, if I order an item on the web the item should be added with a POST because state is changed on the server, the number of items I've added has increased by 1. If I did this with a POST and hit refresh in the browser the browser warns me, if I do it with a GET the browser will simply send the request.
On the server GET vs POST is pure convention, i.e. it's up to me as a developer to ensure that I code the POST on the server to not repeat the call. There are various ways of doing this but that's another question.
To actually answer the question if I use GET or POST to perform the same task there is no performance difference.
You can read the RFC (http://www.w3.org/Protocols/rfc2616/rfc2616.html) for more details.