It makes absolutely no difference. To illustrate why, let's break down the individual changes in direction by 90° segments through the trap, beginning with the vertical drop out the tailpiece:

1. To horizontal
2. To vertical (upward)
3. To horizontal
4. Through any horizontal bends to the tee

None of this changes when you swing the trap pivots. It's always exactly the same sequence. While a fluid dynamics geek could argue the finer points of the forces involved, the variation is negligible.

It makes absolutely no difference. To illustrate why, let's break down the individual changes in direction by 90° segments through the trap, beginning with the vertical drop out the tailpiece:

1. To horizontal
2. To vertical (upward)
3. To horizontal
4. Through any horizontal bends to the tee

None of this changes when you swing the trap pivots. It's always exactly the same sequence. While a fluid dynamics geek could argue the finer points of the forces involved, the variation is negligible for purposes of an unpressurized drain.