Perhaps a good way to begin answering his or her question is to look at the vendors' histories.
Cognos (which started as Quasar) and Information Builders (IBI), the software vendor of the WebFOCUS BI product, have similar origins in the 1970s and then, after a decade or two, experienced a major divergence from each other. Both began as providers of next-generation application development tools hoping to replace the common 3GLs, such as COBOL and PL/1.
Cognos' PowerHouse suite offered tools such as QUIZ for report writing, QUICK for screens, and QTP for batch transaction processing. IBI created the FOCUS language which had facilities similar to those found in Powerhouse, but they also included their own proprietary database structure.
Cognos focused their PowerHouse tools on the midrange market (HP3000, VAX, and AS/400) while IBI went after the mainframes and then expanded to almost every platform imaginable (Tandem and Wang included). IBI also invested heavily in building data adapters to access the various types of data structures.
In the 1980s both Cognos and IBI investigated the artificial intelligence (AI expert system) software market which did not materialize. In 1986, Cognos went public; IBI never did.
When Cognos and IBI tried to move their app dev products to the Wintel platform, they struggled. In the 1990s, both companies released app dev product enhancements to support the new Internet.
The major split between Cognos and IBI came late in the 20th century when Cognos started to make a break with its app dev past. Basically shedding its old PowerHouse midrange tools, Cognos focused instead on new end-user Business Intelligence products running on client-server architectures.
In the early 1990s, Cognos introduced Impromptu for report writing and PowerPlay and a multi-dimensional cube structure for OLAP (online analytical processing). Cognos recently has reworked their BI products for the web, releasing Cognos 8 with new browser-based Studio tools (Report Studio, Analysis Studio, Query Studio, and Metric Studio).
In 2000, Business Week magazine named Cognos one of the Top 100 IT companies in the world, standing right in line behind a different powerhouse -- Microsoft. Cognos grew by acquisitions, buying up vendors of complimentary BI products and applications. Their annual revenues skyrocketed to over $1 billion. In January of 2008, IBM acquired Cognos with plans to double that sales figure.
Bringing in about $300 million each year, IBI remains privately-held with the same owners. Even with a small organization, however, IBI provides top-notch technical support and consistently ranks high for customer service.
The WebFOCUS product, based on the FOCUS 4GL, is truly an enterprise BI tool, able to run on almost any platform and access virtually every data structure. In February of 2001, IBI split out the nuts and bolts of their underlying integration layer, offering it as a separate product under the name iWay Software. Reworking the valuable data adapters to be accessible by SQL (IBM's Structured Query Language) instead of the FOCUS 4GL, IBI created another source of revenue outside of their traditional BI customers.
The Cognos 8 Studios are easy-to-use browser-based tools designed for end users and developers of BI solutions. Providing easy front-ends, however, typically means that some hard work must be done on the back-end. A reporting repository of properly structured data along with multi-dimensional cubes is needed before the end users can start playing. Because of this, Cognos is best suited for an environment with relational data repositories running on a centralized server.
WebFOCUS, on the other hand, is more suited for IT technicians to use to build BI applications. The underlying 4GL has powerful tools for complex reporting and analysis. With WebFOCUS, developers can get "under-the-covers" and manipulate the source application logic, something not possible with most BI tools.
[2010 January comment: of course, Information Builders is working hard to provide easy end-user query and analysis features. See their InfoAssist product.]
As an example, WebFOCUS developers can build row-oriented financial statements, multi-step logical processing, and highly dynamic self-building logic; you would not do this with Cognos. Unlike any other BI product, WebFOCUS can access data scattered across the enterprise on various platforms, pulling things together from different locations to be displayed in the same report output. You still have data locked away in IDMS, IMS, Total, VSAM, Datacom, NonStop SQL, or Model 204? No problem with WebFOCUS.
Those are technical differences. Another consideration is the availability of resources. If you search the Monster job board, you will see close to 900 postings for Cognos people and only about a dozen for WebFOCUS. Because of large differences in customer base and market demand, there are more experienced Cognos developers available.
Which BI product is right for you?
Well, if you have an end-user community needing to build their own reports and queries with minimal outside assistance, and you have an IT database team that could easily create a reporting repository, you should consider Cognos.
On the other hand, if you have a complex environment with several different platforms and databases, and you have an IT development staff that could easily create web applications, you would lean toward WebFOCUS.
Good centralized reporting repository, go with Cognos. Lots of disparate data and some available application developers, go with WebFOCUS.
[An interesting development occurred in January 2010, when IBM began selling WebFOCUS as a web-based BI product for System z DB2 data warehouses. Why would IBM choose WebFOCUS instead of their own IBM Cognos product which also runs on the z platform? See more information here.]
Of course, I have given a simplistic answer to a complicated question. If you want to talk in more detail, contact me.