I know I harvested quite a few deer with my Easton 2219 game getters but not nearly as many of those went right back in the quiver to be used again like my carbons! Either they were nicked or bent or just didn't pass the spin test!
There are more choices out there when it comes to carbon. Different spines so you can fine tune your set up. Different diameters (even larger to around half the size of aluminum). Different weights, different surface finishes to ease arrow pulling/penetration and also they don't bend like aluminum does if you miss in practice. Yes, they can break but, that's less likely than bending aluminum. I'm sure I am missing other difference as well.
My Flat Lines are nearly the same diameter. I've used slightly larger than that as well. They vary in size.
Aluminum arrows are easier to make to tighter tolerances so they are less expensive to make but they will only flex so much before they bend permanently. Aluminum arrows are generally heavier although that may be looked at as an advantage by some if speed is not a concern but a light arrow will shoot flatter. On the flip side, carbon arrows are generally lighter and more expensive to make to tighter tolerances hence the higher price tag. I personally hunt with a light carbon arrow, 8.5 grains per inch and about 400 grains total weight with a 100 gr broadhead, which I always get a pass throughs with. I am shooting 70 lb 30" draw so that helps some. The diameter of the arrow is really not much because your broadhead cuts a pretty big hole in front of the arrow so, while there is more drag it's a very small amount and will not prevent the same shot placement from passing through. Keep in mind I am generalizing because there are examples of pretty much the opposite of what I said. One category that is left is the hybrids such as the full metal jackets mentioned above. They are a carbon tube with an aluminum tube wrapped around that. They are a heavy small diameter arrow that attempts to give you the best of both worlds but if you shoot them enough they will bent too, especially if shooting 3-d targets but you have to shoot them a lot out of a pretty fast bow before a straight target hit will bend them. If you have any questions let me know.