I'm a programmer who knows Python, Ruby and some C who is trying to decide whether to learn GNU Octave or MATLAB. I know that they have a lot in common, but it isn't clear to me how similar the syntax is or even the data structures are. The above link shows several examples where they are syntactically similar or identical. Is this true for the whole language?

I am trying to learn the language in general to do more scientific computing, possibly using some image analysis libraries.

Additionally, is MATLAB worth the cost? 

Answers:

Rather than provide you with a complete list of differences, I'll give you my view on the matter.

If you read carefully the wiki page you provide, you'll often see sentences like "Octave supports both, while MATLAB requires the first" etc. This shows that Octave's developers try to make Octave syntax "superior" to MATLAB's.

This attitude makes Octave lose its purpose completely. The idea behind Octave is (or has become, I should say, see comments below) to have an open source alternative to run m-code. If it tries to be "better", it thus tries to be different, which is not in line with the reasons most people use it for. In my experience, running stuff developed in MATLAB doesn't ever work in one go, except for the really simple, really short stuff -- For any sizable function, I always have to translate a lot of stuff before it works in Octave, if not re-write it from scratch. How this is better, I really don't see... 

Octave and MATLAB are both high-level programming languages and numerical computing environments used for data analysis and visualization. However, there are some differences between the two:

1. License: Octave is an open-source software, whereas MATLAB is a proprietary software.

2. Compatibility: Octave is not fully compatible with MATLAB and may have some differences in the syntax and function outputs.

3. Community: MATLAB has a large community and extensive documentation, whereas Octave has a smaller community and limited resources.

4. Toolboxes: MATLAB has a wide range of toolboxes available, while Octave has limited toolboxes.

5. Performance: MATLAB has better performance compared to Octave, especially for large and complex data sets.

6. User Interface: MATLAB has a more advanced user interface compared to Octave, including features like debugging, code profiling, and integrated development environment.

7. Cost: Octave is free, while MATLAB requires a license, which can be expensive.

Both Octave and MATLAB are used in various industries including engineering, finance, and scientific research. The choice between the two will depend on the specific requirements and budget of the user.