I have never seen any experienced climber tie up a bowline knot starting up with an underhand loop (*). Bowline knots are most typically started with an overhand by flipping the standing part of the rope under the running end.
After the comment by Ben Crowell, it is worth pointing out that starting with an overhand loop determines the position of with the tail end inside assuming that the working end is wrapped around the standing part of the rope anticlockwise. Wrapping the standing part with the running end directed clockwise will render the end on the outside as in this picture in which the initial loop was overhand in both instances:
In any event, the typical result achieved in the most common way of tying up the knot is that the tail end of the rope stays inside of the final bowline as in animatedknots.com:
However, starting off with an underhand loop, passing a bight of the standing end through it, and then threading the end of the rope through the bight, results in a nicer final dressing with the tail end on the outside, as in here. This is the final appearance:
This is not even an esthetic issue with the Yosemite bowline, in which the end is parallel to the standing part of the rope.
Are there any reasons to prefer the most typical way of tying a bowline? Mechanically, they seem to be identically sturdy, but the second knot looks less busy and better dressed. Both of them are equally visually verifiable with the "pierced-tongue" final look.
I just came across this:
which would reformulate the question along the lines of:
Is there only tradition behind the "purists" stand?
(*) An underhand loop is formed when the running or working end of the rope is placed under the standing part of the rope. It results in a running loop when a bight of the standing part is pushed through the loop. The opposite (overhand loop) is formed when the running or working end of the rope is placed over the standing part, resulting in slip loop when a bight of the running end is passed through it.