MATLAB toolbox equivalent for embedded system
First dump it to C/C++, instructions here and profile the application on your computer. neural networks can be rather compute intensive so you need to know how much processing power and what type of processing you need (integer? FP? fixed point? SIMD? etc?).

If you need the network to be trainable while running on your embedded device, then you're stuck developing your own system as MatLab exported code doesn't including the training portions, perhaps based on some external neural network libraries.  I would still start with profiling what you've got to get an idea of what class of device your looking at.

All that being said, the beagleboard is probably a safe bet unless what your doing is very compute intensive, it would also allow you to use most linux libraries.  I used the FANN library for a project maybe 5 years ago and it was good to work with.  I don't know if it will compile for ARM out of the box or if some other library has trumped it recently.