That is certainly a much safer operation because the definition is associated with f, not Abs. For more details take a look at this and this.

Hi Martin

Compare

Table[Abs[i], {i, 249}] // Trace
Table[Abs[i], {i, 250}] // Trace

When the upper bound exceeds 249 Table probably uses a version of Abs that is internal and optimized for long lists.

Lesson: Modifying built-in functions is risky and unpredictable.

What problem are you trying to solve? Perhaps there is a better solution for it rather than this example.