I do both.
if I planned things well with plenty of time, I have the ridge rest pad inside the pack burrito style, or in the summer the Z-rest lite flat 3+3 as back padding.
If I'm in a rush or haven't done good research on a destination, and I overpacked gear inside, then I strap the pad to the outside. but that is not my preference.
Also on day-2 of the trip, wake up early and get on the trail quickly, I might be too lazy to repackage it neatly inside the bag burrito style, so once again, I might strap it to the outside. I've put it under the top compartment T-style, other times strapped length-wise to the right or left side, but now it's unbalanced and annoys me. other times its up side down T horizontal at the outside bottom of the pack.