Quick Reply gives you only a few options for your post like, "Bold", "Italics", "Underline", "Image", "Links" and all the stuff. But Post reply gives you more options, like posting polls, changing your colour font, and all those stuff. ;D
Basically it's just a faster and more basic way to make posts, and it's easier if you just want to write a short message without many details or text edits. ;o