For removal, the owner of a building can contact with a lot of companies. The best qualified company to remove the old fire alarm system, however, is the company that is installing the new system.
Rather than relying on anyone else to remove an old fire alarm system so a new fire alarm system could be installed, the company I worked for always removed the no-longer-used-fire alarm system.
As far as the National Fire Protection Association (NFPA) goes, however, even having a fire alarm system in the first place is the owner's responsibility. The owner only uses a fire alarm company for installation, testing, servicing, and replacement of the fire alarm system.
As well as removing any old panels, devices, and wiring is shown to be the owner's responsibility because the building that the fire alarm system is in belongs to the owner. The NFPA doesn't say who the owner contracts to remove the equipment, that would be up to the agreement between the owner and whoever is going to demo (remove) the old system.
There are a lot of reasons that the company installing the new system should be the ones removing the old system, devices, and wiring.
A fire alarm system is a "Detect Fire and Warn People of Danger" system. Until a new fire alarm system is installed and certified to be working by the fire marshal, the old system has to be in place and be working. If there is a gap in time between shutting down the old system and certifying that the new system is fully functional, just to be able to able to warn people about fire danger, somebody has to be actually looking for fire in the building, 24 hours a day, 7 days a week, throughout the whole building. Yes, the NFPA talks about that.
A number of times, when the company I worked for installed a new parallel fire alarm system, they had the old fire alarm system still working at the same time. Before the fire marshal walked into the building to certify that the new system was working, we (our company) had tested the new system ourselves. (I've heard stories about systems that had not been tested before the fire marshal came in. Usually, the new system wasn't totally working yet, so it wasn't certified by the fire marshal yet. Not a good thing.)
Most of the time, a new fire alarm system has to be working before an old system can be shut down and removed.
To keep from having a time-gap between the shutdown and removal of the old fire alarm system's panels and the installation of the new system's panels, the company removing the old panels has to be the company installing the new panels.
If the company removing the old panels is not the company installing the new panels, there will almost always be a gap of several days (or more) when the building has no fire alarm system. During that gap of time, the fire marshal, the insurance representative, and the building owners all have something to say about an unprotected building. These are all Authorities Having Jurisdiction (AHJ) according to the NFPA. Check the definition of the AHJ in the front of the NFPA Code Book, and also check what is said in the appendix to the NFPA Code Book. There's a whole list of people showing who the AHJs are.
When installing a fire alarm system, it doesn't make sense to try to coordinate work between an un-trained demoing company and the trained in fire alarm system's installation company. If that's tried, a lot of time will be wasted explaining what has to be done for each panel, wire, and device. But then again, only one company at a time can be working in any space, anyhow.
To save a whole bunch of time (time is money), the person qualified to install a new panel should be the one who removes an old panel.
Removal of the Old Wiring and Devices
OK, if the old fire alarm system is shut down before the new wiring or devices like smoke detectors, fire horns and strobes, etc. are installed, it doesn't take much training for any demoing company to remove the old wiring and devices. This can only be done, however, when all of the AHJs agree that the building doesn't need a fire alarm system for a specified time.
The question of who removes the old system and who has to fix the new system is the problem.
The NFPA does say to remove the old wiring. If there are two red wires running next to each other, only the new fire alarm system's installer can properly tell which one is in use and which should be removed. Invariably, if untrained companies try to remove wires, they make mistakes. Then the new fire alarm system's installing company has to come back, figure out what had been removed or cut, and then fix the mistakes.
The same thing goes with removing the old smoke detectors and other devices. To prevent confusion, fire marshals do not want to see any non-working devices. If the other people aren't trained in fire alarm systems, they make mistakes and then the installing company has to come back and fix the mistakes.
The fire alarm system is depended on to save lives. It's a bad idea to let untrained people do anything with the fire alarm system.
Contract and Assumptions
You could say that a contract to install a new fire alarm system would include the removal of the old fire alarm system. Fire alarm design engineers know that, and put that down on paper. If an engineer is involved, demoing (removing) the old system is in the contract.
Most of the time, however, even without engineers, it's a good idea to include demoing the old system in any agreement to install a new fire alarm system. Then the idea of completely replacing a fire alarm system - from the time that any work starts until the time that all work is completed - will be understood by both the owner and the contractor (in this case, the fire alarm company).