Yes, riving is stronger, because you don't sever the grain. Wood is natures composite material. The main thing to understand for the streingth of wood is that the grain of the wood is arranged so that the material flexes allong its leingth without breaking. There is quite a bit of spring in there, and it absorbs vibration very well. When you saw the wood, you end up with shorter sections of continuous grain, and put more stress on the "Glue" that hold the small fibers together. Composites are very interesting materials. Wood is just a naturaly occuring example of one.
As far as SoundGuy's comment about welding cast, I know a lot of excelent welders, including my dad and my FIL. They have both welded cast when college educated experts said it was not recommended. It was just enough to get by, but they don't ever expect it to have the durability it had before. You can seal a leak, but don't ever expect it to hold anything like new. And it is always hit and miss. People think welding is reforming the material. It's not. If your lucky and skilled, you can get close. A repair on wood using the apropriate techniques can aproximate welding in streingth and durrability. More likely than not, if you want original performance the technique would be the same with wood or metal... Throw it away and buy a new piece.