There are many ways to look at things.
The way I analysed the result was like this...
When you dish something out against someone, you have to be prepared to take it back.
We recorded our biggest ever win at Anfield 75 years ago when we won 5-0 on 16th February 1946
On Sunday Liverpool recorded their biggest ever win at Old Trafford with the same score.
The biggest surprise? It took them that long to do so.
You mention about prestige, and it is easy to see where our prestige comes from by looking at what we did before anyone else:
1st English team to win the European Cup
1st English team to win the Champions League
1st English team to win the Premier League
1st English team to win the Club World Cup
1st English team to win the most difficult Treble there is
A lot of fans are not aware of one of the most significant matches ever between Manchester United and Liverpool:
In 1977 Liverpool was on course to win the elusive ‘Holy Grail’ in English club football.
The League, the FA Cup, and the European Cup
They had already won the League, and they were through to the final of the European Cup. They then met us.
Manchester United beat them 2-1 in the FA Cup Final and ended their dreams.
We all know what happened 22 years later... we won the elusive ‘Holy Grail’ and in doing so we became the first and only English club to achieve the feat of winning the League, the FA Cup, and the European Cup in the same season (a record that still stands to this day).
We have climbed Mount Everest.
Liverpool never has.
You can now fully begin to see why Liverpool are not us, and why we are not Liverpool.
In a nutshell the difference between the two football clubs is this:
Manchester United always lead the way..
Liverpool only ever follows after us.