Many companies choose to roll out both an internal and external community at the same time because the incremental work to add additional community is minimal. That being said, if I were to choose one over the other I would start with the customer community.

• Customer communities are easier to get started because you start with a much larger audience and often the bigger the community the more vibrant it is.
• Customer communities are often more homogeneous. For example Dell, Starbucks, and Salesforce have one big community for their customers, where as when you roll out Ideas internally you often have to gather specific requirements and use cases from each department or division.
• The final reason customer communities are often more successful is that customers typically don't have a channel to voice ideas or gain insight into the initiatives your companies are working on. If an employee has a really good idea they can often walk the halls and network to find the right person to pitch it to.

If you have experience rolling out these types of communities, or a follow on question, post a comment below.