I do both, but mostly just place on grill. The hang allows smoke to evenly hit all sides of sausage as it rises. When laying flat, the bottom of sausage sees more smoke... depending on your smoker. Mine is a Smokin It 3.5, with just a 1/2" smoke exit hole, so the whole thing pretty much smokes evenly no matter how I lay the sausage.
Temperature deviations from bottom to top that may exist in your smoker might impact your desision too.
Most items I don't mind light grill marks, or just don't get any--snacksticks are mark free.