It doesn't sound a whole lot different except a little warmer and kind of nasally. The mids are more up front like in a Les Paul. It's a little smoother too, but the Full Shred was never harsh or anything. It feels a little looser which makes it a little more forgiving.
I read somewhere that the Full Shred with an A2 is a Custom Custom with hex poles. I don't know if that's actually true like if it has the same winding, etc..., but it doesn't sound exactly the same. It's still different. I like it so far.