Totally variable, as far as I know. I think there were a lot of veiny bags within the past year; right now it seems to me that there are fewer but that is just my impression.
I have two togo Birkins and they are as veiny as it gets and I love it! I like the texture and depth the veins bring to the leather. I have a Kelly that has very very subtle veins, but it works well with the color which is orange.