A very late response, but your question was so far-reaching that it would be difficult to give a “potted” answer. Also, by now, some of the ground has been covered in posts to the other threads you have started. But to take just one builder, Harrison & Harrison, their organs cover a span of more than a century. There is an undoubted house style, a strongly Romantic bias particularly in the early organs, exemplified by St Mary Redcliffe Bristol (1912) which Martin Cooke suggested you try to visit. Among their hallmarks are their especially sumptuous all draw-stops consoles.
For their modern work, there could be no greater contrast to Redcliffe than their organ at the Royal Festival Hall (1954) and another, not too far from you, St Albans Abbey (1961-62), both in a distinct classical style, and important for the first being designed by Ralph Downes, who was also involved, with Peter Hurford, at St Albans. If you get the chance, go to Coventry Cathedral to hear their exactly contemporary post-WW II magnum opus (also 1961-62) which bridges the gaps between the two stylistic traditions, and is a fine, actually remarkable, example of a top builder’s versatility in producing two such different instruments at the same time.
The subject of “Father Willis” at the Royal Albert.Hall is controversial! - see the separate current thread “Tuning at the Albert Hall”. One could write a book about Willis, but I think you will form your own views. As I said at the outset, it's a big subject.