Perhaps I can shed a bit more light on some of their differences. First I want to talk about their Side B:
Now we already know that Dark Pit's knocks the opponent at an angle, unlike Pit's that knocks them straight up, and does %0.5 more damage than Pit's. Now as far as KO power goes, Pit's was able to kill Mario at %142 earliest on Battlefield (Normal) while Dark Pit's was able to kill Mario at %117 earliest on Battlefield (Normal) when Mario was right at the edge of the stage. When Mario was a bit farther from the edge of the stage, he needed to be at a higher damage percent to KO, but the move still KO'ed earlier than Pit's Upperdash Arm (the distance from the edge makes a difference). So Dark Pit's Electroshock Arm is the better KO move potentially, but Pit's Upperdash Arm is more consistent.
During online play, I noticed another interesting characteristic about Dark Pit's Electroshock Arm. After doing some testing, I found that while opponents are charging a smash attack, if they get hit by Dark Pit's Electroshock Arm, the knockback dramatically increases to the point where the even just the vertical knockback is significantly greater than Pit's. This happened three times when I played online and used Electroshock Arm; 1)star KO'ed Lil Mac at 97% on Corneria 2) star KO'ed Yoshi at 115% on Arena Ferox 3) star KO'ed Mario at 115% on Spirit Train. I don't have video footage for proof at the moment, nor do I know if Pit's Side b has a similar trait. More testing is required; perhaps someone else can verify if they're seeing the same thing. It's fairly situational, but it has helped me in a few matches and would be something different between Pit and Dark Pit. And competitive play does rely quite a bit on using Smash attacks.
I also want to point out one small thing about their arrows. In addition to the differences between their arrows that this thread already mentioned, for Dark Pit's charged arrows, you will begin to see hitstun (the colored trails on the opponents when they're hit) at a much earlier percentage than Pit's (Dark Pit - %140 vs. Mario, Pit - %169 vs. Mario). Not a huge thing, but if Dark Pit can hit enemies with charged arrows at viable KO percentages, that hitstun can help him move in for the kill. In general, I find Pit's uncharged arrows more useful since you can easily change directions with them, but Dark Pit's charged arrows to be more useful as charged arrows for both are much faster, so Pit's control will make it hard to know where the arrow will actually go.
Another thing I've noticed is the differences with some of their custom moves. It turns out that Dark Pit's Striking Flight does 0.5% more damage than Pit's (similar to their Side b) and KO's a little bit earlier than Pit's (Dark Pit's KO'ed Mario in the middle of Battlefield (Normal) at %155 while Pit's KO'ed Mario at %163 in the same scenario). Also Dark Pit's Piercing Bow is significantly stronger than Pit's in terms of knockback (KO'ed Mario at %171 on Battlefield (Normal) compared to Pit's KOing Mario at %191 on Battlefield (Normal), of course the usablity of this move is a different issue.
Also, I find Dark Pit *feels* a bit heavier/slower than Pit, more noticeably in the air. I'm not sure why though; I've verified that their running speed, falling speed, weight, and jump height are the same, but I can feel a difference between them in that Pit seems just a tad easier to control. Again, I don't know why this is the case, maybe it's attack speed or lag :S
Anywho, that's my input, hope it helps.