Practically there's little difference between the two, both are essentially just image filters.
The CUA tonemap is mega old, probably from a time before postmagic was created and is a fixed filter whereas with LUTs theres 1000's of LUTs out there so you have much more flexibility to find the right filter for your scene/shots.
The cua tonemap will also occasionally cause issues with other assets so a LUT is preferable unless you need the exact filter the tonemap provides.