The problem I see with privatisation is that money has to be found to pay shareholders. Nationalisation would work better _as long as_ the government is prepared to put money into it, if it isn't it's probably little better than privatisation. There needs to be a 'public service' ethos in public transport, which costs money, from taxation, which sadly in the right-leaning political environment we live in now is perhaps not politically acceptable.
One thing I will say is that trains seemed to be less delayed and overcrowded during the 80s (when I used them on a daily basis Mon-Fri to go to school). Another thing I will say is that on continental Europe, where trains are nationalised, trains appear to be cheaper and more integrated with buses.
Agree that the 'old stock' argument is weak. It's just a coincidence to do with the timing of the last mass stock replacement in the 1960s. In the late BR days of let's say 1992, there was a hell of a lot of stock about 20 to 30 years old. Given the lifetime of typical MUs seems to be around 35 years, the stock was 'too young' to be replaced at that time. I suspect it would have been replaced in the early 21st century had BR remained. The mid 2020s is going to be like the early 1990s in that respect, there will be plenty of by-then-old Sprinter and Networker era stock I suspect - and that will be (presumably) under a still privatised railway. Even stock like the 377s and 444/450s is going to be 20+ years old by then.
So my gut feeling would go nationalised, though if it has to be private, I would advocate one single and regulated company, or at least a very small number of companies a la Big Four. The big problem with public transport in this country is the lack of integration. We have an ex-Southern Region with different and incompatible classes of third-rail EMU. Contrast that with BR days when CIGs, CEPs, VEPs, HAPs and EBPs could all work with each other. We have the Southern fragmented into different companies. Why not just one? Why the hell do we need South Eastern, Govia Southern (or whatever they call themselves this month) and South Western? Why not, at the very least, a Greater Southern Railway?
I'd also have integrated buses with through ticketing. Combined train-bus journeys, or even bus journeys with two operators, are disproportionately expensive. Basically we need more of a public-service ethos in public transport, this is something decidedly lacking in the UK compared to some continental countries. Perhaps we as a nation simply dislike paying tax to fund such a thing.