Internal Hosting (You use your Own Server)

External Hosting (We host the application)

It is on site, if you want to see your server this is the only way you will be able to see it. Availability: interestingly enough, despite many firm's misgivings about losing control over their IT equipment, there is a lot to be said to having a professional firm that has the deep pockets needed for redundant systems and tested disaster recovery plans run your IT infrastructure. If you work at a small or even a medium sized firm, this may be especially valuable to you.
You need to do work and if it is onsite you have to check on it. Flexibility: currently most cloud computing service providers don't require users to sign long term contracts that lock them in. This makes it easy to quickly get more cloud resources when your firm needs them.
Bandwidth, you need to move large files into the system continuously and have very poor upload speed. No up front licensing or equipment cost to get up and running.
The Cloud scares you. You do not have to buy a server that will last a year, you get what you need in the short term and scale it up and down as required.