Looks to me like a bunch of particle effects…you’ve got your “sparks” that drift and fall, your “comets” that woosh down the screen…etc. Play around with CC Particle World and/or Trapcode’s Particular (if you have it.)
For the words – you could just create a particle system with alot of particles falling, and then use the layer above it as a “Track Matte” to act like a big stencil over that layer.