The earlier vessels had a flat deck above the bridge windows that extended aft to the area around the mast.Frankly, the "new" bridge look to be exactly the same height as the old bridge to me. Both main bridges structures are exactly 2 decks high, with navigation bridge windows at the second deck level.
The new design has a higher level above the bridge windows that extends aft to the main mast.
This is what people are talking about when thy say the "new" bridge. Over the actual bridge the deck is not higher, and that higher deck extends back to the deck house around the mast.
You can see it in the new picture above the windows on the bridge. On the old design the top of the deck is right over the windows. On the newer design it is a couple of feet higher.
OLDER DESIGN
NEW DESIGN