An answer is long overdue here and this is my short answer...depends.
Now, for a far more detailed answer. What it depends on for me personally is, whats my personnel? Do i have a big shooter in the middle, a powerful shot on the wing, gifted skaters, a combo, defensive specialist, etc.?
Here are some examples I've used over time and my reasoning for doing so.
Carson (R )-Turgeon(L)-Recchi(L)
All 3 have 4/5 shots, Carson and Turgeon are 4/4 skaters, Recchi a 5/4. I have a big shooter in the middle, and big shooter on each wing. Carson is a bit heavier, its tough to get to the net with him consistently, so its more useful to be able to feed him where its easier to do one-timers and let go of his slap shot. I liked Recchi on his forehand as well because he carried the puck a lot, so i wanted the slapshot as an option to keep the defense honest, also, hes fast enough to deke and his shot is strong enough to where the backhander isnt an issue.
Hawerchuk is a playmaker, not much of a shooter, so its pretty useless to keep him on his off wing to utitlize his slapper. Guys would typically sag off of Hawerchuk, try to take away passing lanes to my two snipers, so when there was open ice it was much easier and efficient to attack the net on hawerchuks natural side. Another strength to him playing his natural side was that he could use his forwhand pass to feed Sandstroms forehand...5 passer to 5/5 shooter can be devestating. Robitiaille was used on his off wing for similar reasons to Recchi/Carson.
Kelly Miller(L)-Kontos(L)-Holik (R )
Miller had 4/4 speed and 3/3 shot, again, fairly useless to try and utilize his slapper a lot, much easier to use his skating to either crash the net or feed Kontos. Also, if i wanted to cut into the middle for a floater, i could do so, or i could fake the floater and stuff it in far post with a quick backhander. As for Holik, he was just a guy who could take and give a hit, and skate a little, he had no stand out skills with the puck. The most effective thing with Holik was crash the net and get a near post deke goal, much easier to do on his forehand than his back.
Classic Spring 09:
Some different reasoning here then the other all Lefty line. Turgeon has 4/4 speed and 3/2 shot, not much reason for him to be on his off wing or in the middle. Easier for him to have the room to use his speed and make plays on his natural wing. Baker has the best shot, thus he goes into the middle. The other 3 are more or less the same player, average skaters, lack of shooting. The reason to put them on their off wing? Due to their inability to slap shot effectively or deke consistently, its easier to feed them one-timers if they get into position since theoretically, they are shooting on a goalie who will more likely be out of position than not.
In general, what my constant goal was with my offense was being able to attack in as many ways as possible. If you got a big shooter who can go on a wing, put him there, open that option up, but, if there is a dearth of shooters on the wing, dont pigeon hole your self into difficult situations by putting them on their off wing.