The issue is not really with Advanced vs Casual, it's more so to do with the players themselves. While writing long-posts is cool and all, it doesn't make you an advanced roleplayer, it just makes you someone who can write long posts. This has been a source of argument among my group in the past, where a few particular people insisted that better players made longer posts, something that simply isn't true. The "purity" of roleplaying lies solely in how the details are presented, and whether or not story has been expanded, something that can be done in both long and short posts. Don't think of Casual as short-posts, think of it more as a relaxed environment focused on concise posting. Just the same as one shouldn't immediately think of Advanced as advanced. Advanced really isn't that advanced from time to time, and really should just be called "Regulated", since that's what it is. Though if you really want an answer as to which section is purer than the other, I would have to say neither and vote for 1x1. That's speaking from my own experiences with groups over the last few months, and how I have found that you can accomplish far more with a good partner in a 1x1 than a group of "Advanced" roleplayers. It's sort of the reason why I've decided to stop joining group RPs and focus solely on the 1x1s I have going.

Really at the end of it, though, if you're trying to figure out which style of RP is purer than the other, you might be doing this hobby for the wrong reasons. Just my two pence.