Well, by the look of the particle stream, it looks to me like they were most likely made with Trapcode Particular.
Once can tell by the fact that as the particles go faster they spread apart and look more like dots instead of a stream of particles.

To achieve this in Maya, search the help for Particle GOALS.

You can animate the goal object to move/wiggle a little bit with a rand() expression on its' position to give the Directional emitter stream some curves and random directional vector changes, but still have some controllable movement.

Try that as a test and let us know how that turned out for you.

PS: Will it be easier than doing it in post with Particular? Probably not, but it will be more fun