When does it makes senses to use Dot-Product as similarity measure instead of Cosine?
Borrowing from this Quora answer -- which includes some concrete examples of when you might prefer one measure over the other -- it comes down to whether you care about taking the magnitude of the vectors into account. This is highly domain-specific, but the example used there is in information retrieval, where magnitude represents the length of the documents in question. The dot product will take the document length into account, whereas the cosine similarity will not. 

In general, you will want to have good reasons specific to your problem space to use one over the other.