I want to create very thick and defined white smoke. Should I model it with displacement or use the smoke simulator? Note: this is a still image.
It's a lot easier to get realistic results with the smoke simulator, however it will take longer.
A quick (and rather terrible) attempt at mesh smoke:
To create the mesh smoke I used a subsurfed cube with a displace and a remesh modifier, which I extruded randomly and duplicated around in edit mode.
There are some tricks to getting smoke sim bake times down for a still, for example you can use a faster time scale and/or a quick moving particle system as the emitter in order to get the smoke into position in a smaller number of frames.
To get a nice thick white smoke, try using larger number of volume bounces and a lot of light. In the above images I used 5 volume bounces and a strength 5 sun lamp.
You can set the bounces in Render settings > Light paths:
Also make sure you have a pretty dense volume shader with scattering.
For a smoke sim a simple way to tweak the density is with a multiply node: