I don't see why anyone would want to use ANIMAL based glues on PLANT fibers, though. It'll work, and it's strong. But wood glue is formulated for wood, and jute is going to have WAY more in common with wood than collagen-based animal fibers like sinew or hide.
I'm a bit late with this reply... Had to look it up.
Wood glue, at least regular (eg titebond) is liquid hide glue to which urea was added to keep it liquid and stop it from gelling at room temperature. So essentially, there will be hardly any difference. Hide glue granules or gelatin leaves do have a longer shelf life. Moreover, you can control viscosity and tackiness more by adding granules, reducing the volume (evaporation) or adding water.
But bonding properties are very similar.
J