I know this is probably one of the most basic questions out there, but what are the advantages of sitting on a stool compared to standing? I saw CSO the other day, and Alex Hanna along with several other section members were sitting with a lower endpin, and a more upright bass. Most of the section plays French bow, along with sitting down. Does the now play as a factor when deciding whether to sit or stand? I like to stand for solo, and I'm not sure for when I play in the symphony.
In a very generalized nutshell: standing is easier for the right hand, sitting is easier for the left.
When you stand, your ability to physically maneuver around the instrument is enhanced. Your entire body can move around as needed, and it is easier to adjust the instrument's position to adapt to your needs. However, your left hand will have to help stabilize the instrument on top of everything else it has to do. This can make shifting, and the resultant intonation, especially problematic, particularly in low positions. You can minimize these shortcomings with good posture and a bent endpin, but you'll still need to address the underlying problem.
Sitting frees up the left hand to do its thing, but this causes its own problems. Sitting cuts you off from your legs, which can otherwise be useful for leverage. Your ability to get around the instrument is significantly lessened, which can be a big problem if you have short arms or are generally a smaller person.
You can minimize these problems by taking an appropriate stance and posture. I set my stool to lean slightly forward, and sit on my sitz-bone on the edge of the seat so that if I were to lean forward (without the bass) I would naturally stand up. This keeps my legs engaged and allows a little more flexibility from the waist up. I also use a foam block under my left foot. This does two things: (1) keeps my knee at a more comfortable 90-degree angle rather than bent inward toward the stool's rung, and (2) allows me to adjust everything so that only my knee makes contact with the edge of the bass, which prevents the "damping" issue addressed above.
Most professional orchestra players sit, particularly in the US. It's partly tradition, partly for comfort (nobody wants to stand through a Wagner opera), and partly because the majority of what they do is in lower registers, which requires a free left hand.