The new Assault is completely re-worked. Almost only thing in common with the old, is that it is seven stages.
The seven stages increase in difficulty. For every stage you can try with a different plane. Some planes will come with a 50 % increased reward. Raiden, will always (currently as of July 2018) come with a 100 % increased reward.
You can bring brobots and devices to the battles.
Here are videos of the different stages, higher to lower.
Stage 7 Buzzsaw, Dodgy, Legatus
Stage 6 Patriot, Dodgy, Legatus
Stage 5 Raiden, Dodgy, Squire
Stage 4 Blitzer, Dodgy, Squire
Stage 3 Eagle, Dodgy, Squire
Stage 2 Wraith, Dodgy, Squire
Stage 1 Greataxe, Dodgy, Squire