I bought a bottle of Titebond III a few months ago, but haven't had a chance to try it yet. But several years ago, I did a test to determine which glue would give the most invisible joint in walnut.
I planed some black walnut and cut it into small samples which I then glued with Acraglass, West System Epoxy, Titebond II, a polyurethane (Gorilla type) glue, and a few others.Titebond II gave the most invisible joint, followed by the epoxies. The polyurethane is said to be better in oil contaminated wood, and gave a pretty invisible joint. But any glue squeeze-out acted like a sealer and took a lot of sanding to permit an even finish or staining.
I then broke some of my glued test pieces by clamping them in a vise and smacking them with a hammer. I don't recall the exact results, but I do recall that the Titebond II joint was stronger than the wood. I'll use dowels or pins if I can hide them under a lock plate or trigger guard, etc. But for most cracks or splits in clean wood, I won't lose any sleep with Titebond II or a good epoxy properly applied and clamped.The polyurethane was very strong as well, but the excess was messy and harder to clean up.