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…
Also, if you learn Octave, there’s a lot of syntax allowed in Octave that’s not allowed in MATLAB. Meaning — code written in Octave often does not work in MATLAB without numerous conversions. It’s also not compatible the other way around!
I could go on: The MathWorks has many toolboxes for MATLAB, there’s Simulink and its related products for which there really is no equivalent in Octave (yes, you’d have to pay for all that. But often your employer/school does that anyway, and well, it at least exists), proven compliance with several industry standards, testing tools, validation tools, requirement management systems, report generation, a much larger community & user base, etc., etc., etc. MATLAB is only a small part of something much larger. Octave is…just Octave.
So, my advice:
- Find out if your school will pay for MATLAB. Often they will.
- If they don’t, and if you can scrape together the money, buy MATLAB and learn to use it properly. In the long run it’s the better decision.
- If you really can’t get the money — use Octave, but learn MATLAB’s syntax and stay away from Octave-only syntax. (see note)
Why this last point? Because in the sciences, there are often large code bases entirely written in MATLAB. There are professors, engineers, students, professional coders, lots and lots of people who know all the intricate gory details of MATLAB, and not so much of Octave.
If you get a new job, and everyone in your new office speaks Spanish, it’s kind of cocky to demand of everyone that they start speaking English from then on, simply because you don’t speak/like Spanish. Same with MATLAB and Octave.
Note: Octave can be run in “traditional mode” (by including the –traditional flag when starting Octave) which makes it give an error when certain Octave-only syntax is used.