Head above the parapet time here - I'm going to side with Shallyman. IIRC, the United/Liverpool rivalry started to spice up a bit in the late seventies, when Liverpool started to win the league more regularly (they won it three times in the 12 years in the top flight under Shankly, then 8 times in 11 seasons from 1975/6 onwards). It became quite nasty from both sides pretty quickly, as well. The Manc derby was different in that it was the game that you'd get merciless stick for at school if you lost, and certainly in the late seventies, it was a huge event on both sides. But then, the match could definitely go either way, City had more Wembley appearances and the like through the seventies, and by the time we were averaging home gates of over 40K between 76 and 78, that probably meant that the Manchester region had fairly equal numbers of match-going fans for both clubs. (United's gates were bigger than ours, but even then, they used to draw a lot of out-of-towners).
What really turned things round was that City were so poor for so long. After our victory in the derby at Maine Road in February 1981, we won one more competitive fixture against United in the next 21 years and 9 months. After we went down in 1983, we played outside the top flight for nine of the next 20 seasons, so for nearly 50% of the time, there wasn't even a proper Manchester derby, just the odd friendly or testimonial. In the light of that, it's hardly surprising that the occasion lost its edge and United fans started to regard Liverpool as the bigger game - and it happened very quickly after we failed to offer any meaningful derby challenge.
If, over the coming years, we have City and United competing with each other in the title race and having more major Cup games against one another while Liverpool predominantly finish in the Europa League places, things will probably start to change. However, it will take some time, I'd have thought. We certainly always got to them a bit even when we were shit and they were winning everything in sight. Any protestations that they saw us irrelevant to them were given the lie by things like that banner, while you could often hear lots of signing about us when they played in one of their rare (arf!) televised games. But I think we're deluding ourselves a little if we suggest that the derby has, in the last couple of decades or a bit more, generally been the game even local United fans would regard as their biggest.
Can't say it matters to me anyway. We're not the City of old any more and they know they've got a hell of a fight if they want to be the more successful club in Manchester these days. That's what counts for me now.
