I have never used ultimate cut, but I have used Autoglym 03B and found it to be like liquid sand paper...they also make 02B and 04B (one is more aggresive, the other less aggresive...I forget which is which). I believe the bottle says it is adequate for removing 1200 grit sanding marks.
Just be careful!! And please keep in mind that a follow-up polish with a lighter pad/polish might do the trick, rather than go the opposite direction (on extremely soft paints like Honda black that is)