Some advantages to having a custom application built for you...

Your applicaiton is built from the ground up and you are involved in the design process from the beginning.
You are involved in the process of fine-tuning the application to meet your business needs. You'll spend less time learning the software because you will have helped design and implement it from the start.
Often the cost is a fraction of a 'Vertical' Package.
As your business needs change, the software can change with it. New features can be added, un-needed features can be removed. As your business grows the software can grow with it.
If you don't like the way something works, it can be changed!