Updated
A High Cube container is built to an external height of 2 896 mm (9 ft 6 in) instead of the standard 2 591 mm (8 ft 6 in). Length and width are unchanged, so it occupies the same ground area, stacks with standard containers and is handled by the same equipment.
What you get is 2 698 mm of internal height instead of 2 393 mm, and roughly 13% more volume. What you pay is a small premium on the unit and about 300 mm more overall height on the road.
Why High Cube has become the default
The extra height costs very little to build and adds nearly nine cubic metres on a 40ft unit, so shipping lines standardised on it. The majority of newbuild 40ft production is now High Cube, which means better availability, more predictable pricing and — sometimes — a used High Cube costing less than a scarcer standard-height 40ft.
Note that the same is not true at 20ft: 20ft High Cube is a genuinely scarce type in Europe.
The road height question
A High Cube on a standard chassis sits about 300 mm higher than a standard container and can approach 4.3 m overall vehicle height. Motorway clearance is rarely the issue; site entrances, low bridges on the final approach and car park decks are.
Measure the lowest point on the route, not the gate. This is the only real reason to specify standard height instead.
The gooseneck tunnel
Most 40ft High Cubes have a recess in the underside of the floor at the door end, so the container can sit low on a gooseneck chassis. It does not reduce usable interior space, but it does mean the underside is not flat — set the container down on level bearers rather than bridging it across uneven blocks.