Hi Alex,
Here is one way using the example from the attached notebook
t1 = {0, 5, 4, 6, 7}
t2 = {0, 1, 3}
Abs[Subtract @@ PadRight[{t2, t1}]][[;; Min[Length@t1, Length@t2]]]
(* {0, 4, 1} *)
The order does not matter
Abs[Subtract @@ PadRight[{t1, t2}]][[;; Min[Length@t1, Length@t2]]]
(* {0, 4, 1} *)
I have not done any timing to see how efficient it is. How long are the lists you are working with?