Prior to Beeching, what were the main considerations a passenger used to say get from Manchester to London. When one could go to Euston, Marylebone or St Pancras? Was the seating/in train services quite variant between each railway?
I think you need to go back a little bit before Beeching to really put your question - but it is one that I've pondered, or rather, wondered about more from the commercial, or operator's angle.
In particular, you choose Manchester as your example, which is perhaps not the best. The reason I say this is because the GC was never going to compete on schedules from London (unless, perhaps, you lived next to one of the stations in the suburbs). It just went too far round at the northern end, heading north east at Leicester towards Nottingham and then north-west via Sheffield and Penistone.
And I don't even think the Midland really stood much chance against the LNW after the grouping in terms of timings: apart from being a bit slower for the first 130 miles or so, the last 60, including Ambergate to Chinley, were so difficult as to ruin its chances as a real competitor once average running speeds began to rise. (* More later)
More interesting would be to study route choices like London to Rugby, Leicester, Nottingham and Sheffield, London to Birmingham and maybe, London to Exeter.
I suspect London - Rugby the LNW won hands down vs GC because of frequency.
I suspect London - Leicester and Nottingham, the Midland won on frequency and 'first at the game' - though Nottingham was also served by the GN.
There is also the question of location of stations - particularly in London, where eg Marylebone was relatively 'out of town' and not particularly well connected vs Euston, St Pancras and Kings Cross. In the case of traffic to the West Country, Waterloo probably had the advantage here (and to some extent, still has, despite the far slower schedules from Exeter).
The London - Birmingham - Wolverhampton contest is probably the most evenly balanced of the big ones, and I don't know who was winning that prior to 1960.
* Which brings us back to the Midland vs LNW and the question: why didn't the LMS management simply rationalise things, ie downgrade the Midland service from 1923, rather like the LMR did in 1966 with electrification of the LNW?
Well, perhaps they did to some extent (any experts out there can comment?), but I suspect it may come down to the implications of Taunton's post regarding the GC services to Manchester, that is, prior to the mass production of cars starting in the mid-1950s, there was still significant traffic generated mid-route to justify the use of these long-distance trains. (nb also the continued use of the Thames-Clyde and Waverley + sleepers on the slower Midland lines to Scotland well into the 60s.)
With the advent of the family owned car from c 1955, traffic from these intermediate journeys dropped away (because people used their cars) while traffic to and from London was rising, or at worst, more or less constant.
One probably needs to add into the mix the sharp drop in forces traffic from 1945 onwards.
Of course, Paddington - Brum and St Pancras - Manchester (and even the GC to some extent) did get boosted from 1957 - 66, but this was only a temporary blip caused by diversions for LNW electrification.