kerf- smooth expansion and constriction of air pressurization, less chance of port noise. Difficult to build. (there's also 45 flared ports)
slot- standard, easy, gets loud, usually recommended. Slots are easy to get very precise port area and tuning.
aeroport-round ports have less internal resistance due to the fact that being round has less internal surface per port area than a slot. They also work like a kerf if they are flared, allows for smooth airflow.
octoport-just looks cool. Not very difficult to build, get's closer to a round port than a slot.
Typically the more round or perfectly square the port, the better, IMO