PROS:
1) allows for lower installed height of engine in car providing a lower center of gravity. This helps in Cobras, but is mostly associated with GT40's. In fact, an FE in a GT40 virtually REQUIRES a dry sump to fit the engine in the compartment. The new Ford GT uses a dry sump today for the same reason.
2) provides better
oil control, as mentioned. The pickup never gets uncovered, no matter how extreme or extended the side load on the car. Also allows MORE
oil to be on onboard, some systems measure
oil quantity in gallons. This tends to keep the oil cooler, which leads into one of the cons (see complexity below).
3) a dry sump pump can have multiple stages by design, and not all stages need be concerned with pumping oil. Some stages of the pump can be dedicated to evacuation which aids ring-sealing and can increase horsepower (if the rest of the parts in the engine are selected to take advantage of it).
CONS:
1) complex...external (usually) pump with a belt drive needs to be mounted. A LARGE oil tank needs to find a home somewhere. Oil lines running hither and thither. Because of the volume of oil, it may require a heater for the tank to warm up the oil. The tank may need either two chambers or a system of breathers or some other means to prevent foaming of the oil.
2) costly...all in, you're probably looking at something north of $2K.
3) reliability? the pump is usually driven by a belt, which is subject to damage from road debris or just age. When it goes, you have no oil flow (so along with the oil reservior, add in the space needed for something like an Accusump).
4) unsightly...tanks, lines, hoses, breathers, pumps, belts, all snaking or stuck on or sticking up or cramming up your engine compartment. Just my opinion on this. Some might think it looks good.
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The above relates to the old style dry sump systems. GM and Ford both have new systems which are much cleaner looking, don't rely on belt drives (usually driven directly off the crank), and less complex that are installed on standard production vehicles today. But they are designed for the modular and LS(1 and 6) engine families so I don't know how relevant this advance is to you.
HTH