As an ESRI professional, you obviously know the server product from this vendor that can be compared to GeoServer well. It is called ArcGIS for Server and in many ways it can play the same role as that of GeoServer, and the opposite is true as well, of course.

Undoubtedly, the big question for you is: why should I use GeoServer and not stand safely on the vendor side, leveraging on integration with the other software members of the big ArcGIS family?

Listening to colleagues, asking to experts, and browsing on the Internet, you'll find a lot of different answers to this question, often supported by strong arguments and somehow by a religious and fanatic approach.

There are a few benchmarks available on the Internet that compare performances of GeoServer and other open source map servers versus ArcGIS for Server. Although they're not definitely authoritative, a reasonably objective advantage of GeoServer and its OS cousins on ArcGIS for Server is recognizable.

Anyway, I don't think that your choice should overestimate the importance of its performance. I'm sorry but my answer to your original question is another question: why should you choose a particular piece of software?

This may sound puzzling, so let me elaborate a bit on the topic. Let's say you are an IT architect and a customer asked you to design a solution for a GIS portal. Of course, in that specific case, you have to give him or her a detailed response, containing specific software that'll be used for data publication. Also, as a professional, you'll arrive to the solution by accurately considering all requirements and constraints that can be inferred from the talks and surveying what is already up and running at the customer site.

Then, a specific answer to what the software best suited for the task is should exist in any specific case. However, if you consider the question from a more general point of view, you should be aware that a map server, which is the best choice for any specific case, does not exist.

You may find that the licensing costs a limit in some case or the performances in some other cases will lead you to a different choice. Also, as in any other job, the best tool is often the one you know better, and this is quite true when you are in a hurry and your customer can't wait to have the site up and running.

So the right approach, although a little bit generic, is to keep your mind open and try to pick the right tool for any scenario.

However, a general answer does exist. It's not about the vendor or the name of the piece of software you're going to use; it's about the way the components or your system communicate among them and with external systems. It's about standard protocol.

This is a crucial consideration for any GIS architect or developer; nevertheless, if you're going to use an ESRI suite of products or open source tools, you should create your system with special care to expose data with open standards.