A lot of times to satisfy planning permission they want to see a clear distinction between old and new.
An ultra modern stadium whilst preserving a lot of the historic walls, gates and floors would likely be a good option all round.
Trying to make a new building fit in to a historic surrounding (unless its a restoration) doesn't always sit well, as what's old and important sometimes gets muddled up with what's brand new.
A good example is the Albert docks that was a restoration project, so they tried to keep the building looking very similar to how they originally looked, from the outside anyway.
Then when Liverpool 1 was built they didn't try and keep that theme going, because it was new builds, so they have made L1 ultra modern, and they both compliment each other.