Reading up more about Catterick (couple of news articles from The Guardian and The Echo, plus a book by Sawyer), I feel that is definitely where the divergence between the status of the two clubs begins.
While Shankly was telling the world he was building a “bastion of invincibility”, Catterick was shutting the doors of the club to the outside world. The RS were the first team on Match of the Day (vs Arsenal), while Catterick was against the club being shown on tv.
The 60s was such a pivotal moment in pop culture, of which sport is a big player. United and the RS really took off in that period (Shankly as mentioned was the trigger for the RS, while United’s was the story of the Busby babes and the Munich crash, followed by the Busby leading a team (including first celebrity footballer George Best) to the EC a decade after the disaster). Whether it’s tag lines such as This is Anfield, or Theatre of Dreams, the mystique/stature/identity of both clubs in the media has remained since then.
There’s also another factor, legacy. From what I’ve read thus far Catterick is seen as a ‘chequebook’ manager, able to bring in top players under Moores. When he left, that was it, there was nothing for his successor to pick up. Of course that his successor was the god awful Billy Bingham didn’t help. With Shankly it’s the opposite, the boot room. A management structure he had set in place that was able to continue from where he left off, similar training methods and playing style, and he also left his successor a load of top young talent (Keegan, Toshack, Clemence, Heighway, Hughes, Thompson etc.).
It’s as though Catterick’s name is stuck in the period of time in which he worked, a relic, unlike the likes of Shankly, Busby, Stein who just go on. The manager being the face of the club, Catterick being introverted made the club introverted, Shankly being an extrovert made the RS extroverted. You can see this today with the difference in appearance of banners, flags etc. Colour is also one of the thing that attracts fans.
On a side note to this, the way Catterick treated Alex Young was a disgrace. Told by Catterick he would receive 1k when he left the club, then when he went to get the money Catterick tells him you should have got it down in writing. Young walked out and never spoke to him again, surprised he didn’t chin him.