The only difference is that one is rectangular and one is round. It does not allow a larger airflow with the same size box and port, because if you keep the port the same legth you must also keep it the same area.
The advantages are that slot ports can be made much larger than round ports. A 3 inch round port has about 7.07 in^2 of port area. Say you wanted to run 42 in^2 of port area for a big box, you'd have to use 6 of those ports. Or you could build a slot port that is 3 inches wide and 14 inches tall. That will give you the same tuning (as long as length is properly calculated), and do so with a single port. Slot ports are also "easier" to fit in some applications, for you can run them along an outter wall and bend them around corners and such. Plus you don't have to buy anything extra when building the box, cause they are made out of wood too!!
So in general, if you had some huge box it would make no difference if you ran a 10 inch round port or a 15.6 x 5 inch slot port. But finding 10" tubing for a round port isn't easy, or cheap, so slot ports are the way to go. You wouldn't want to run 25 2 inch round ports to get that area either, as the friction between the port walls and the air has an affect on tuning. This is negligable when talking about a few ports (less than 4 approx.), but has a large effect when you get up to a lot of ports like that.