These lists generally skew to recent success anyways... I have no trouble with Barcelona being placed a hair ahead of us.
The one redeeming factor for our European record is our success in UEFA Cup/EL when it was arguably harder to win than European Cup/CL.
But I'd still place at 3-4 behind Madrid and Barcelona. Probably ahead of Milan, just due to crushing them so badly domestically, and on a level with Bayern. It's splitting hairs below Real Madrid though, for Barcelona, Juventus, Bayern, Milan. It's quite difficult to account for things like domestic league strength and competition, as well as the advent of super teams and lack of competitiveness in this post-2000 modern era. Etc.