Free / Libre / Open Source Software (FLOSS) Benefits

Here are benefits from the point of view of various stakeholders of FLOSS services.

For Organizations (using the software)

Avoid vendor lock-in: Manage in-house with your IT team, or outsource, with a choice of service providers. You can change service providers without changing the technology.
Host your data where you want.
Better control of your data: Open standards are great. However, they cover a very small part of all the data that is managed. Data migration from one application to another is typically costly, and some data is lost because the data structures don't neatly line up. Thus, predominantly, data management is inherently tied to the software used to manage it, so all software has some level of lock-in, but if the software is not FLOSS (that is, if it is proprietary software), there is a higher level of lock-in.
Transparency: You can follow the software development process (who is contributing, bug reports, etc.)

For Service Providers

Easier promotion — users find projects via directories such as https://www.openhub.net/ and then, once they pick a project, they can find service providers via the project.
- It's a great way to demonstrate competence. When your contributions are valued by the community, your clients can trust that they are in good hands (even if the client doesn't have the expertise to evaluate directly)
Some clients have requirements to have access to the source code.
It's easier to find expertise. Within organizations, other service providers, upstream software, etc.
If circumstances change, and you no longer can or want to provide services to a client, it's much easier to responsibly transfer to a new service provider.

For Team Members (of organizations or service providers)

When changing jobs, skills and experience are re-usable.
Experience with Open Source software increases demand, and thus employment opportunities (employer knows they can deploy quickly a solution with no license fee, while experience on in-house software has little value)
The same software can be used on personal or volunteer projects, at no cost.
Team members get to collaborate with others all over the world, and it leads to increased feedback and emulation, and thus increased skill level.
Since developers work on publicly accessible source code, it permits to showcase their work, increasing employment opportunities.

For All

Avoid license hassles. Beyond the cost of licenses, all the time to manage, audit and comply can be saved.
Avoid licensing concerns impacting deployment decisions. All users can have accounts. Install as many copies of the software as you want.
Economies of scale (there is an investment to learn the software, but then each new deployment doesn't have a license cost).
Innovation: because the source is shared, all the best available experts are collaborating.
- If the source is closed or in an open core model, or in a plugin model, expertise is fragmented.
Security: Open source code can be audited independently.
You aren't limited to what the software publisher has planned.
- A multitude of sources are improving the software, with a diversity of use cases and points of view, contributing to the building of resilient systems.
It's possible to contribute (upstream) enhancements, and not just bug reports and feature requests.

In addition to FLOSS considerations, it's much better to collaborate and avoid the duplication and fragmentation caused by third-party plugins: http://pluginproblems.com/ .