Knockdown
Sprayed compound flattened with a knife into a soft mottled pattern. It is the Florida standard, it hides minor imperfections in the drywall beneath, and it is forgiving of a ceiling that has been patched over forty years. Faster and cheaper than smooth.
Smooth
A level-five finish: skim-coated, sanded flat and painted. It looks contemporary and it is unforgiving. Every joint, screw and undulation shows under raking light from a window or a downlight, so it needs more coats and more sanding. On a ceiling that has been repaired repeatedly, smooth can cost noticeably more than the quote you were expecting.
Knockdown ceiling texture and future repairs
Worth thinking about before you choose smooth. A knockdown ceiling can be patched almost invisibly by someone who can match the spray density. A level-five smooth ceiling cannot: any future repair, from a leak or a light fitting, shows as a flat patch under raking light and usually means refinishing the whole plane. That is a real cost in a house where things get opened up.
Which to pick
If the ceiling is flat and the house is being modernised throughout, smooth. If it is patchy, or the budget is finite and better spent elsewhere, knockdown is not a compromise so much as the regional norm.