My recollection is that Octave is significantly slower than Matlab, and some quick googling on benchmarks [1] suggests that it is (was?) as slow or slower than R.
I've complained before that Octave is the wrong solution to the Matlab problem, and if you aren't attached to one of the many fine Matlab toolkits, you're likely better served translating to a more expressive language, like Python+Numpy+Scipy.
Octave is Matlab clone, in fact Octave developers openly say that except for some special cases, any difference between Octave and Matlab is a bug.
The biggest difference between Matlab and Octave is JIT compiler in Matlab, which does incredibly good job at vectorizing simple (or sometimes even not-so simple) loops.
I think it's fair to say that Octave performance is very close to a Matlab in a pre-JIT time.
There's also a huge difference in toolboxes, profiling, sparse matrix operations, parallel computing and many-many more. In these areas I'm afraid Octave is light-years behind Matlab.
However, you still can do a lot of useful simple stuff with Octave and it's free! Matlab-like syntax is really, really cool then it comes to vectorized operations. So probably these two reasons determined Andrew Ng's choice of Octave as a main environment for ml-class. Huge win for Octave I guess. This might spur some interest in the development, attract new people to the product. I think it's a well-deserved success for John W Eaton and other people who develop(ed) Octave all these years.
I agree with your take on Octave performance relative to Matlab. The Matlab parallel toolbox is getting more and more useful in a multicore world.
As you note, the Matlab profiler is very nice. You can zero in on the 80% of the 80/20 tradeoff very fast, during your usual development cycle. It's as simple as:
>> profile on
>> do_something
>> profile report
and you get a nice graphical/textual report on time usage in everything do_something called.
This is not true. They strive for Matlab language compatibility, but none of them refers to Octave as a "Matlab clone", nor are they working on cloning Matlab, nor was the project started to become a matlab clone. It is like calling Linux a "Unix clone".
I've complained before that Octave is the wrong solution to the Matlab problem, and if you aren't attached to one of the many fine Matlab toolkits, you're likely better served translating to a more expressive language, like Python+Numpy+Scipy.
[1] http://sciviews.org/benchmark/