I don't worry about strength. Every glue I use is stronger than wood.
One thing to keep in mind about TBIII is that it dries really hard. No flex to speak of. That can make some wood movement issues more serious.
When I built my front entry door I used TBIII to glue the frame pieces around the glass. With TBII I can let it set most of the way and then slice the squeeze out free with a chisel plane or whatever. The TBIII dried hard as a rock. I probably spent 3 or 4 hours cleaning up all of those panels. They had to be perfect since that's the show side.
One more... When Alex Snodgrass was here doing the 3D cutting board he used TBII. I asked him why and he said with the wood movement in an end grain board, he'd had failures using TBIII when the environment changed rapidly. He's sponsored by Titebond, so I suspect he has pretty good inside info on using it.
Half of what we read or hear about finishing is right. We just don’t know which half! — Bob Flexner