Does it matter (texture of meat) if you cut it straight down or on an angle ?
Absolutly. Cutting brisket properly is just as important as how you cook it.
The muscle fibers in a brisket are very long and tough. If you were to cut with the grain of the meat, it would be stringy and hard to chew. The idea is to cut directly across the grain, which is why it gets cut at a very specific angle. I actually used the photo of the uncooked brisket as a reference for the grain pattern when I began slicing.
Brisket is actually two different muscles, called the flat and the point (also called the deckle). The flat is generally leaner, the point fattier. They are separated by a layer of fat. Each muscle has its own grain direction, so the flat gets sliced in a completely different way than the point.
When sliced properly, the cross section will show being made up as little sections (the actual muscle fibers) separated by intermuscular fat.