Not sure what you mean by "For years the All Blacks would always pip the Springboks at the end of games", because from 2010 to 2018, New Zealand set South Africa aside very comfortably in almost every game, sometimes even destroying it, like the 40-3 (2011), 15-57 (2016) and 57-0 (2017) thrashings. Granted, there were a couple of close encounters, like in 2013 (27-38 at Ellis Park) or 2015 (RC and the RWC semifinal), but they were rather the exception than the rule.
The only notable difference in terms of New Zealand, IMO, is that back then they probably had the best bench in world rugby, which is not the case anymore. Yesterday, the bench was woeful, didn't add anything, while giving away some stupid penalties at the end of the game.