650 grains, is 650 grains......but the others have already stated the differences with faster recovery of carbon so I won't rehash that discussion.
Me personally, I have used woodies, carbons, and aluminum arrow shafts. All will kill just fine, but I always keep coming back to carbons for the straightness factor and quicker recovery factor. The spine is also a more absolute or stable aspect of carbon for me. Woodies if tuned or sanded correctly for spine can be matched perfectly with each other as a set of hunting arrows, but carbon takes all that elbow work and meticulous crafting out of the equation.
Some guys really enjoy putting alot into crafting their own woodies and I applaud them for it, I've even done it myself but getting older now and don't have the time or energy to mess with it so that's why I went back to carbons.
My CX Predators with 190gr. up front fly like darts and pack one heck of a punch when they slam into my target, and I can't wait to get one into a whitetail.
I am going to experiment with river cane and my own 190gr. trade points, but that will be for a different bow set up all together. So I'm not totally turned off of natural arrow shafting by any means, I love river cane and everything about it.