We were assigned a handicap room as a last minute upgrade. We did not need this type of cabin but were reassured that all pax who needed handicap accommodations had them on our cruise.
Our cabin was on the Dawn Princess, but I think you can expect much the same accommodation on any line. Here's what we had. A slightly larger cabin door and foyer and more room at the base of the beds (for wheelchair turning circumference). The bathroom also had a larger door and a flat threshold (most ship cabin bathrooms have a step-over threshold). The bathroom is also larger, again to accommodate the turning of a wheelchair. The shower is designed so that you can roll your chair right in and transfer to a fold down bench. There are additional grab bars as well and the area beneath the sink is free from obstructions. Beyond these items, I noticed no other differences. Storage space is the same and the furniture in the room is the same as in other cabins. I recall that the Dawn had space beneath the beds which made it nice for tucking luggage out of site.
The only negative I have is that without any lip on the shower, sometimes the drain did not drain as quickly as you might want and water would roll out onto the floor. So you need to be watchful of that.