I have not used Matlab much lately, although I used it regularly about 5 to 10 years ago. I have little experience with Octave. I did try it on linux a few years ago, and it did appear to have have a reasonably large subset of Matlab's function. Simple Matlab scripts would run on Octave without any change. More complicated programs and packages likely need some hand fix-up to run. The Octave FAQ had (has?) a fairly lengthy listing of compatibility issues, including Octave extensions that are not reverse compatible. Octave seems to me to be more Matlab compatible (a better clone) than Scilab, for example.
My problem with Octave is that I have never been able to build and/or install it on Mac OS X. No pre-compiled (dmg) packages seem to be available for OS X 10.7 or 10.8. My attempt to install Ocatve using Macports a few months ago was a dismal failure. Octave, at least on the Mac, does not seem to be supported as well as other Gnu software packages.
The situation is better on at least some linux distributions, where there are binary packages available. I don't know the status of Octave on Windows, but some colleagues of mine have used it under Cygwin.
Thanks for responding, Gerry. Your information is very helpful, especially concerning the installation of Octave. The instructions for installation on OSX found on the Octave web page looked pretty daunting so I held off on trying to install it until I learned more. Based on your experience, I am glad I did. You have probably saved me a lot of frustration and wasted time.