A word. Think of the steak fibers as a bunch of bamboo skewers, looslely glued together into a solid unit. When you cut a thin slice perpendicular to the skewer lengths, you end up with very little glue holding them together, and they are easily seperated. If you cut them at an angle (bias slicing), the amount of glue holding the bunch together is greater, and the moment of force becomes less, making it harder to seperate the bamboo skewers.
This is analogus to the meat fiber. Cutting against the grain, vertically will give you the most tender meat, and the smallest slices. So, you must ballance the meat quality and the bias slicing to achieve satisfactory results. I made a brisket last week on the grill, following tried and true methods of slow, moist-heat, and cooking until medium rare. The meat was still tough. I tried cutting against the grain, on the bias. It was Ok for me, but not good for my wife. She requires more tender meat than do I. I had to cut it vertacally to make it tender enough for her.
So, cook it, cut it at different angles until you get the result you desire.
Seeeeya; Goodweed of the North