Good question, upstream cast for me or better put, quartered up so I get a good dead drift. For downstream, on large stretches of water I always let the fly coast down until it starts waking or gets pulled under. I've caught enough fish that way that it became a habit over time.
On small streams you do sometimes run into a feeding fish that can only be reached with a down stream approach. Here it becomes a matter of developing a style that will get results.