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Once, when I was much smaller and dumber I didn't know quick reply existed, and I was always using post reply.
Now I forget that post reply exists, instead.
It depends if my post would be long or not. If I want to use any CSS styling or BB codes in my posts, I would usually prefer going advanced than just staying in this little box. However, I usually use the quick reply option at the bottom of a page because of my procrastination of clicking post reply and waiting for it to load. That is too much for me.
I start almost every post in the Quick Reply box. It's much more convenient.
But if I'm writing a post that starts getting pretty long, I'll usually preview it before posting so I'll go advanced. Very rarely, I'll know from the get-go that my post is going to be long and I'll hit post reply to do it. Also when I'm quoting/multi-quoting, I use the full reply for, well, obvious reasons. I never remember the "quote in quick reply" button and prefer to see what I'm quoting while I'm writing anyway.
I use quick reply, since I have just set my font to what I like. All I have to do is type. Simple. Although if I am writing something large or quoting someone then I will use the post reply.