Never had a fly line with a loop for the backing ... have had fly lines with the loop for the leader connection and in that case I went with a loop to loop connection, using a plain over hand loop knot for the leader - larger leader material like 25# mono and above, use a perfection loop. But as for a loop for the backing, I suppose that would work as well, but that would be a big hassle for making a loop to loop - would you not have to pull the entire length of either the fly line or the backing through the loop ...?

As for attaching the fly line to the backing, in that the line dia. is considerable between the fly line and that of the backing (assuming there's no loop involved), I use a sheet bend knot. Small, strong knot, and the odds of that knot ever getting to the exposed are enormous (at least for the fish I catch!) -

http://www.netknots.com/rope_knots/sheet-bend/