I've not used Matlab but I've used Octave (during the ml class from Andrew Ng) and it wasn't too awful. Occasionally very frustrating though so if Matlab solves those frustrations I could see it being worth it if you're going to spend time in it!
I've used both before. Matlab in my CompSci BS and MS and Octave in my professional career.
I'm just making the point that your critique of Octave seems a little harsh, and to the Leyman skews the reality - that Octave is an open source alternative. Yes, a little rough around the edges if you intend to use the visual aspects of the tool, but for matrix multiplication etc it has its use cases.
The parts you say are good about Octave are EXACTLY the stuff I use Python and R for. If you want to use a Matlab library or toolkit, maybe cut in paste some code from a paper, do a quick 'what if' thing -- Octave just doesn't cut it.
(My point in speaking up here isn't to diss Octave it's to re-center the reality around Matlab.)
Love open source, glad they're doing it, much love to the devs -- and life is just too fucking short. If you're broke or screwing around--ok, maybe. If you're sitting in it more than an hour a week, maybe Photoshop is worth the $10/month vs GIMP, dig?
And if you're in school and get it for free or are interested in getting up to speed with the state of the art in machine learning and qualify for the personal license at under 200 bucks? I can't think of a better tool.