GET is for reads, POST is for writes. If you're CURL'ing to another service you need to use the method their API tells you to - if they wrote it correctly choosing your own method won't work. Also, GET is limited to around 32K on most server setups, while POST can get way up there. Even on servers where that is changed, GET is rarely upped to the point of POST.
Also bear in mind that proxy servers may, at their discretion, cache GET requests. That could be troublesome.