We don't have a comparative analysis for Fisheye and Bitbucket Server, but we'd be happy to outline some of the main differences for you here.

Fisheye is our repository browsing tool that will allow you index and search a variety of SCMs, like Subversion, Perforce, Git, etc... It provides a read-only window into your source code giving you the ability to generate reports, like a commit graph, and search for buried methods and functions hidden within your file structures. Its strength lies in its ability to report from your repository activity and search across SCM platforms. It doesn't, however, allow you to manage your source code - this is where Bitbucket Server comes into play.

Bitbucket Server is our Git repository management tool that allows you to lock down your repositories with 4 levels of permissions, collaborate on your code through the use of pull requests, and create custom functionality using a full REST API. Bitbucket Server is the platform that hosts your source code, as opposed to just providing read access like Fisheye. I suggest looking over our Bitbucket Server QuickStart Guide to get an idea of how it can fit into your development workflow.

The choice to use one, or both tools, is highly dependent on the types of requirements you'd like to fulfill, and the ecosystem you currently have in place. I suggest giving both products a try using our free 30 day evaluation licenses. The best way to determine what's right for you is to give it a shot!