This may be a little more info than you wanted but....
Firstly, let's assume that the following statements refer to well-designed boats where keel sizes, shapes and angles have been calculated specifically for the boats that they have been attached to.
The primary function of the modern keel is stability. The weight of the keel counteracts the lateral forces imposed on the sails and the rigging by the wind, allowing the boat to remain relatively upright.
Hence a keel has a certain weight, and this weight is carried sufficiently low, to provide the boat with enough stability to keep it close enough to level in order to obtain optimum performance in the range of windspeeds that the designer expects it to encounter. There is an additional margin of safety that is designed into the boat in order to ensure that it is likely to survive occasional winds that are stronger than anticipated.
Almost as important as this function of stability is the function of providing directional integrity. The keel, in conjunction with the rudder, is largely responsible for the boat's ability to maintain a course. This is particularly true in the case of shallower, flatter hulls, such as are often found today.
When you look at a wing or a fin keel, you will find that the keel has a foil shape, similar to that of an airplane wing, or a sail. Just as a wing or sail provide lift, the keel does as well. If a boat were able to sail completely level, and if there were no current in the water, there would be no need for this shaping as it is properly a symmetrical foil that is mounted exactly in the center of the boat, thus when the boat is level there is a null lift effect - i.e.: both sides are generating the same lift force, cancelling each other out.
But, because boats heel and because there are subsurface currents in the water, as the boat leans and the keel presents an angle to oncoming water, the keel acts like the wing of a plane to some extent, and provides an amount of lift to the hull, theoretically reducing wetted surface area, cutting down on friction and allowing the boat to sail faster.
The keels that provide the most lift to windward are the long, thin keels such as those found on Mumm and Mount Gay racing boats. Keel design is a subscience of yacht design and becomes quite complicated, taking into account hull shape, wind speed, hull loading, drag and flexibility.
In the case of a wing keel, there are additional lift forces and turbulence factors that come into play. Whereas a fin keel offers no lift when a boat is running directly downwind, the wing keel is shaped so that the horizontal projections, which are also foil shaped, provide some lift to the boat in the same manner as the fin does when it is angled on a boat sailing to windward.
In order for this to work properly, the angle of incidence of the wings has to be such that the keel does not create a stalling effect. Basically, if the boat is not going fast enough, the keel does not provide any lift and it does nothing but create additional drag. But when the boat is moving at sufficient speed, the wing keel will lift the boat up and allow it to sail more quickly.
When a boat heels as it sails to windward, the vertical fin area of the wing keel provides lift in the same manner as the fin keel does, but the wings themselves generate lift in a direction that is roughly 90 degrees to that generated by the fin portion.
As a result, it is very difficult for a boat equipped with a wing keel to sail quite as close to the wind, as a fin keeler, as the keel is generating what amounts to additional leeway.
Additionally, the wings create turbulence in the water flow at the point where they are attached to the fin, not a significant amount but it is there.
Where a boat is offered with two or three keel options, wing keels and shoal keels also tend to be heavier than the fins, as they are usually shorter, hence the righting moment they generate is less because the weight they carry is closer to the fulcrum (waterline) of the boat.
Finally, the surface area of a wing keel is usually greater than that of a fin or shoal keel, which creates additional drag.
In the end, it comes down to a matter of personal preference. As with everything else in life it is a compromise and there are benefits to both wings and fins.
I personally feel that a well-designed wing keel allows for a better all-around boat, but there are many who will argue this point bitterly. In order to notice the difference in performance between a fin and a correctly proportioned wing, you've got to be racing to windward pretty consistently and at my age the only racing on our boat is from the cockpit to the head and then to the fridge.
I enjoy the offwind bonus and shorter draft.