I mean, why would the shape change?
Here's the modern helmet maker for the UK fire services: http://www.rosenbauer.co.uk/equipment/helmets/
Modern materials are lighter and more stable, thus need less material, which gives more flexibility to move.
Also the tasks changed. These days there are less fires, but more kinds of "technical assistance" and when there is fire water usage is more targeted and restricted.
Iconic british firefighter helmet use to be leather than metal. There are very good reason why they have been changed. The wikipedia page explains the differences over time and culture: