What's important to remember is that Ra's al Ghul in the Nolanverse and Ra's al Ghul in the Arrowverse are not the same characters; although superficially similar, they have different aspirations and motivations.
Ra's in the Dark Knight trilogy has very unclear goals, but in general he seems to be (or see himself as) a kind of moral guardian for the world. When explaining Bruce's purpose in the League of Shadows, Watanabe-Ra's says:
Fake Ra's: Gotham's time has come. Like Constantinople or Rome before it the city has become a breeding ground for suffering and injustice. It is beyond saving and must be allowed to die.
And later, when Neeson-Ra's is explaining why, exactly, he's going to let Gotham destroy itself, he says:
Ra's: Whenever a civilization reaches the pinnacle of its decadence, we come to restore the balance.
Again, it's unclear exactly what his grand scheme is, but it's a primarily social motivation; the people of Gotham are corrupt and decadent, so they must die.
As for Ra's in the Arrowverse, season 3, Episode 4 ("The Magician") has some exposition from al Ghul's daughter Nyssa that helps explain this. According to her, the League has a strict code of conduct, which Malcolm's Undertaking violated. She doesn't expand on what those are, but I would speculate from historical sources that they involve not killing the innocent.
The League is likely based on, if not a literal descendant of, the most famous group of assassins (And the origin of the word "assassin"): the Hashshashin1. There's some evidence that the group had a code of conduct, especially given that they never targeted civilians. Since much of the point of assassination is to avoid large-scale bloodshed, this seems like a reasonable policy for such a group, and I highly suspect that the League has adopted it.
We get more of an answer in season 3, Episode 9 "The Climb", from the mouth of the Demon himself (emphasis mine):
Ra's al Ghul: I was eleven years old when I killed my first man. I remember the look on his face when the light went out behind his eyes. Such a subtle change, almost imperceptible, between life and death. And I felt ashamed. I'd stolen from that man the most precious gift of all: life. But I also felt something else: pride, because I had taken up arms against someone who sought to do ill against my family, and I realized what I had done was necessary. You see, I had replaced evil with death. And that is what the League exists to do.
A possible explanation is that the League opposes killing the innocent, and Malcolm's massive collateral damage overrode any evil he may have killed in the Undertaking.
This is speculation again, but it occurred to me recently that another possible explanation is that Ra's didn't consider the Glades to be evil. It's pretty firmly established in season 1 that Merlyn's Undertaking is revenge for the murder of his wife. While that's certainly sad, it's ultimately hard to argue that a crime-ridden and impoverished region of a major city is evil (or even to blame) for being crime-ridden and impoverished.
Ra's may be thinking along the same lines as Oliver was in season 1: the "evil" in Starling City was caused by the self-serving corporate executives and corrupt politicians running the city into the ground for their own gain. The same people, ironically, who Malcolm recruited to help realize his Undertaking.
So it would appear that the main difference is that Ra's in the Arrowverse has more faith in the people; he believes in pruning the dead branches so the tree can heal itself. Compare to Ra's in the Nolanverse, who would rather torch the whole forest.
1 This is the group that the Assassin Order from the Assassin's Creed game series is based on