Often times by the time a client gets to finding me, they have reached a point where they are ready to throw away their entire web infrastructure: both their corporate website and their intranet. They hope that one well executed product selection can solve both problems. When approached by this kind of prospective client I am careful to set the expectation that this hope is probably not realistic — not impossible, just not realistic. That said, there are a few conditions where putting your intranet and external website on one stack does work. Here are the criteria that I use.
The intranet is informational rather than collaborative. Different people mean different things when they say the word "intranet." For some, an intranet is just a collection of web pages that only employees can see. Others think of tools and workspaces that allow employees to collaborate and get things done. If you had the latter in mind, chances are you will be looking for a document management, ECM, or portal system like Sharepoint for knowledge worker collaboration. These systems are technically capable of pure web publishing but that is not their strength. Your website management team will feel constrained by a platform that treats web publishing as an afterthought. If you think of your employees and customers/prospects simply as different audiences that you need to publish to, a single platform may work just fine.
The company has other platforms on which to build specialized, dynamic web applications. Sooner or later (or probably already) your company is going to need to develop content-oriented web applications and your WCMS is a logical place to start. However, these web applications are likely to introduce the most demanding and specialized requirements. It is quite possible that the union of your intranet and external website application requirements filter out every viable CMS — or at least force some painful compromises. If you have an alternative stack on which to build your fancy custom applications (possibly pulling content from your WCMS) and can let your WCMS focus on simple web publishing, you greatly increase the chance that you can comfortably support both internal and external publishing.
The corporate website and intranet are owned by one communications group. Today you may be able to align your intranet and external publishing needs; but will they stay aligned? How will you arbitrate between the competing priorities of the intranet and marketing website? What if those priorities don't just compete for resources but actually conflict with each other? Things can get ugly when two different departments with different goals argue over what feature needs to be added next. These decisions get a lot easier if both the intranet and external website are owned by one communications group. Companies that are structured this way are usually small and can benefit the most from sharing the infrastructure cost between the intranet and extranet. Having the intranet owned by a communications group also pretty much ensures that criterion 1 is satisfied.
If your company meets these criteria, there is a good possibility that one instance of one CMS platform could serve you quite well. Otherwise, I would recommend doing one of your two projects and then putting the product that you used on the short list of products to consider for the other. If it turns out that the one platform supports the requirements of the second project, buy another instance of the software (hopefully at a discount) and start a new project to implement it. Take advantage of code and idea re-use but don't let that constrain the flexibility and agility that you need to achieve your goals.