This, gentlemen, is Colonel Sebastian Moran, once of Her Majesty’s Indian Army

So the question is why did Moran end up in the Indian army? He's often characterised as being in the British army but that isn't what it says in the canon and I think this actually makes him far more interesting and is far more suggestive and gives him far more depth than if he had just been said to have been in the British army. The thing about the Indian army then seems to be that it was basically where you went if you couldn't get into the British army; it was looked down on by the British army. But this is a man with an Eton education, from a family which would seem to be pretty respected and respectable and have money. Surely he could have got into the British army? (The purchasing of commissions wasn't ended until 1871 after all) So what was it about Moran that caused him to end up in the Indian army? My answer is kind of threefold really:

1 He wanted to get the hell away from Augustus Moran and joining the Indian army seemed to give him more chance of getting away and staying away from him. Plus had he joined the British army he would probably have had the shadow of Morans before him (not just his father) hanging over him all the time. 
2 He was regarded as 'not quite a gentleman'. Yes he came from a good family and was born in London and his father was the former British minister to Persia and there was money there but then there's always something a bit off about him. Maybe it's the Irish name. Maybe it's the fact he doesn't treat everyone who is supposedly beneath him with contempt and always seems a bit too friendly with the lower classes and the natives. Maybe it's that he doesn't really speak correctly and is rather too prone to talking like a commoner (I still absolutely think portraying Moran with a 'common' accent as in AGoS despite his canonical background is completely right).
3 He had the wrong attitude for the British army - yes he has the sense of superiority but he was too smart-mouthed, too prone to challenging those he was meant to show deference towards; he despises the monarchy and the aristocracy; he's unapologetically not religious; he hated a lot of the rituals and customs and habits and the absurdity of trying to recreate Britain complete with all its inane pastimes and gossip and suchlike in India; he was a loner really, not a team player.

I think really Moran would never have fit in the British army and he barely even fit in the Indian one (he got driven to 'retire' from that after all). I actually still think he was never really cut out to be a soldier or an officer at all - yes he was intelligent and courageous as well as being a brilliant marksman and he cared about his men and I believe totally he's a good leader, but he really wasn't deferent enough to those above him; he was not a patriot; he hated the army overall and the empire and those who treated him and his men like pawns and cannon fodder; he hated the queen and all she represented; he hated Britain; he was also I believe not hugely racist and didn't think anyone with brown or black skin was inherently inferior and perhaps worst of all I think he absolutely questioned the right of the British to even be in some of these other countries. Plus he was queer and there was a certain degree of acceptance of homosexual behaviour in the army perhaps what with so many officers being ex public school boys but I think Moran was so unapologetically and unashamedly queer and his queerness was a sort of open secret and that was not really the done thing. It's inevitable that he would get driven out of even the Indian army prematurely, because he needed to be with someone like Moriarty, not something like the army.