The big difference between the two is that the Weaver stance uses isometric tension between the firing hand and the support hand. Done properly, this helps control recoil and pull the gun back on target for the next shot.
I say again: big difference is ISOMETERIC TENSION, firing hand pushes, support hand pulls, for the Weaver stance.
In the classic Weaver stance, the firing arm elbow is locked out for greater rigidity, but there are so many "schools" out there with their little dinky "modified Weaver stances", that this is not neccessarily taught any more.
The classic Weaver stance may be hard to assume in winter clothing, and is easier for dangling arm gorillas than other body types.
The Isoceles is basically a naturally assumed two handed grip, though some schools may tout certain further specifics.
In general, because the Weaver stance requires the support hand to be in front of the pistol grip. this causes the support leg to be forward a bit, and the firing side leg to trail.
Many instructors are very anal about getting it just right.