Bias tape is lighter and stretchier than gros grain. It is easier to form to the curves of a cat cut but probably would not stand up as long depending on use. For example I would not suggest using bias tape for tie out loops.
If you are looking for an alternative to gros grain and can't find the bias tape you want you might want to consider twill tape. Still lighter and easier to handle than gros grain (IMO) it has the same kind of weave pattern as gros grain. Bias tape is woven with the pattern on a diagonal slant to the edges. Hence the term bias tape. Twill tape is woven with the ridge patterns running straight acorss the tape edge to edge. It is a more robust product but not as heftyas gros grain.