The control panel is often put on the right side as a default, with the intent of catering to a predominantly right-handed species, and sometimes to a right-handed culture. But that's only when there aren't other considerations, and there are lots of other considerations.
There are definitely site and installation dependencies. Some elevator cars are not mounted central with the doorways, leading to asymmetric car shapes, with a single door opening to the left, or to the right, while others have two doors parting in the middle. (The parking garage I use has three elevators, where the middle is asymmetric and has the panel on the left side, while the other two cars are symmetric and have the panels on their right sides.) Some sites maximize the width of cargo by opening the doors the full width of the car, meaning the panel must be mounted on a side wall, where it's visible as you walk in, eliminating the guesswork.
For installations where money is less of a concern than user convenience, they may install two panels, one on each side of the car. This is often the case in high end buildings. It's also common in hospitals, where usability, efficiency, and time considerations are always rated highly, and you don't want to delay someone by making them search for the panel. Two panels may also be chosen for reliability, as there are always redundant buttons and lights. When there are two panels, one will have all of the fire safety features and controls, while the other is simply a duplicate floor selection panel.
Two panels may also be more desirable in elevators that service the general public, where strangers are less likely to communicate than two co-workers working for a common employer. Of course actual public buildings are often built on a stringent budget to appease taxpayers, and two panels may be a luxury they forgo.