Uefa used to rank stadia as being 4* or 5*. Although capacity was one of the factors it also included grading of facilities not only at the ground (i.e. pitch size and condition, floodlights, corporate seats, hospitality, enough space for cameras/photographers, TV studios and media facilities, journalist space, appropriate dressing room and dugout facilities for teams and officials, CCTV and security ect) but also in the surrounding area (transport links, airport capacity, 4/5* hotel bed space ect). Just because you could seat 60k didn't automatically mean you could make the grade and a lot of old stadia therefore failed. When building from scratch these regulations are now taken into account and I am guessing in order to host matches at championships the stadia must meet the characteristics. Attempting to host world cup matches in Hull/Portsmouth/Nottingham ect may prove problematic due to the infrastucture issues regarding transport.
Another factor when holding tounaments would be available space for fan parks near the ground, and a lot of historic grounds in the UK are pretty much landlocked in industrial or housing estates which would cause issues here. This is another reason why new-builds are out of town. The staduim in Istanbul used for finals recently took a lot of critisism for being out of town. It was originally built as a centrepiece for an Olympic Bid which was never successful and therefore the anticipated development around the ground never happened.
The main distinction between the two was capacity, 4* stadia could hold more that 40,000 and are eligable to host the Uefa Cup final, 5* stadia were of a higher capacity (can't recall if it was 50k+ or 55k+), although this has since been changed to an overall UEFA elite staduim status regardless of capacity. in practice, because of the numbers of fans involved it is unlikely that a some of the smaller stadia will get the cance to host finals as UEFA are swithing to using only the megastadia for finals