Let’s get the basics out of the way first: a ported cabinet has a port, or opening, that is either in the front or the rear of the cabinet. A sealed cabinet has no ports, and is pretty much air tight. So that’s the physical difference; what is the sonic difference?
Sealed bass cabinets, much like closed-back guitar cabinets, tend to be tighter, punchier, and more articulate. The trapped air acts as a “spring,” which helps control the movement of the speaker and also acts as a sort of built-in “limiter.” This may also mean that they may be less efficient pushing out lower frequencies and require a higher wattage amp to achieve a given volume level.
Ported cabinets (also known as “bass-reflex” cabinets) use their ports to “tune” the cabinet to a particular low-frequency band, usually optimized for the speaker inside. The port creates more output at that low frequency, meaning a ported cabinet can sound louder at the same power level than a sealed cabinet. However, if the port isn’t tuned properly, the bass can get “tubby” and the transients less distinct.
Which is better for you depends on your amp, your performance space and gig requirements, and the sound you’re going for.