From my experience, it doesn't matter too much which leather glue you use, Barge, Weldwood, Masters, etc if you are gluing leather to leather and stitching. In regards to shoes and glue, it seems to matter quite a bit, especially if you are just planning on gluing the man-made sole material on and aren't going to stitch it in place. Then the glue really matters. If you are looking at this from a shoe making point of view, I'd suggest you go and talk to a couple of cobblers in your area and ask them about their experiences.
Whichever glue you end up using, if it's not water based, make sure your shop is set up to use the glue and you have the proper PPE for it. If the glue can meld plastic to leather, just imagine what its doing to your lungs.