We are ussually just above or below France in terms of population and GDP. I would say the biggest transport infrastructure differences between our cities are the age of the railways and the "demolition" works between 1939 and 1945. I am not convinced that an underground network would suit Manchester. A Picc-Vic HS2-NPR tunnel would be good for regional and intercity services but adding an immediate station would add to the cost and slow services down. Metrolink is very good at serving the whole city centre and being at street level is a significant part of ease of use.
It is unfortunate that the drive towards post-war rebuilding in Manchester, as in so many other places, was utterly, fatally fixated on roads. A public transport-based alternatibe would have led to less damage being done to the urban fabric, as well as providing us with a better network today. If someone had given me a clean sheet of paper in 1945 (or 1948), I might have suggested taking advantage of the existing connections by building an inner rail loop using ovwrhead lines around the northern and eastern edges of the city centre. I woild probably also have focused long-distance travel on Victoria, given its then-size, and built additional approach lines as necessary. I would also have made sure the tram.and trolleybus networks of Manchester and surrounding towns were maintained and expanded.
Starting from where we are now, I'd agree that the first tunnel built should be an east-west tunnel for long-distance (not just high speed) services between the existing main stations, with the spare capacity on existing lines used for a suburban heavy rail system.
Eventually, I'd like to see the Altrincham, Bury and Oldham lines restored to heavy rail (perhaps with Metrolink providing local services for some or all of the way to Altrincham, using the unused 4 track alignments and bits of street running), with a north-south local rail tunnel, and the remaining Metrolink infrastructure refocused into a denser network, making more use of street running.
This is because I want to see Manchester (and everywhere else in Britain) provided with as extensive and good quality public transport as possible, rather than being fobbed off with whatever's cheapest.