I'm a full time FileMaker developer. I think hosting with the right hosting company can be a great solution and takes off your plate some issues such as keeping SSL certificates up and maintaining backups. The smaller the company, the more this seems to appeal to them. While I often recommend hosting, most of my clients choose to host it in-house. There are several reasons, probably the primary one being that performance is clearly better on your own LAN than over the internet. Many of the companies I work with also are reluctant to host data externally for security reasons. Some companies just like to physically know where there data is located and feel uncomfortable with cloud solutions. While I would not consider that a valid excuse, it is a reality of some companies.
Cloud hosting solutions tend to cost less because you are not purchasing and buying hardware and software and the costs are often being shared across multiple other companies hosting on the same server. Of course the more other companies hosting on the same server, the slower your performance, but in general, cloud hosting is cheaper than hosting in-house.
One benefit of running a server locally is the flexibility to decide when you can take the server down and do upgrades instead of relying on schedules dictated by a hosting company.
If security is really important to you, then you will have more control of security tools to monitor attacks and/or computer forensics if you are hacked for which you would not control on a hosting company.
Probably the most common reason I have for requiring in-house hosting is because of the need of additional functionality through server plugins. Most hosting companies are not going to allow you to put plugins on their servers. But I find more and more clients need them particularly for web APIs such as Google Charting or cloud mapping or talk to other web services through http posts, etc. FileMaker does have the Insert from URL, but it is not as robust and does not include the security you can get in plugins like Base Elements or Monkey Bread Software. Other functionality some need are plugins for credit card processing or graphics manipulation on the server. Alternatively you can do the plugin work on the client machines. But more and more my clients like to keep the client machines clean with no special plugins and any special functionality is done on the server and not the clients. It makes desktop maintenance a lot easier.
If you have another server locally that FileMaker is directly interacting with, then hosting FileMaker server on the same switch as the other server is a much better performer. This could be integrating with maybe some MySQL web database or an accounting database on Microsoft SQL Server or Oracle, etc.
If you can keep things simple without additional plugins and speed is not critical and the staff size is small, then cloud hosting can clearly be a better solution. But when you run into some of these other issues, sometimes one of them bumps you over the need to start hosting locally.
Just taking a look back through your original question... wow.... You are using FileMaker 10??? Oh my.... all kinds of security issues come to mind. Obviously Triple8 has newer servers for hosting. But FileMaker 10 is not supported by FileMaker anymore and is really out in the wild as far as security. My first advice is to upgrade your software both on your hosted server and on your clients. But maybe this is why you are going through this question of what to upgrade to. FileMaker made a significant security update at FMS 13.0v9 and anything before then would be out of the question for me. I encourage you look for a solution that upgrades you to FileMaker 14.