Hopefully the 8.1 update will address the tile moving problem. My desktop at home has 8.1, but no touch screen. My work tablet is running 8, not 8.1, so I am familiar with how troublesome it is (I pretty much have to use the stylus that came with it--it has a button on the side that essentially right-clicks).
You tap and hold tiles on the 8.1 Preview on the RT to move them, so the experience is just like Windows Phone.
I'm sure the RTM is the same, but we won't find out (at least on RT) until October.