Most full keel boats will have a shallower draft and more wetted surface area so they are a little slower (more drag) and can't point quite as high into the wind. However, they have a much more comfortable motion in heavy seas, as they have a more v shaped hull and do not pond into heavy seas. Some full keel boats are so poorly designed though, that they can't sail into the wind at all. These boats are more like motorsailers etc... Hardin Voyager, Formosa. Well designed full keel boats are usually more rugged and their rudders are better protected from grounding damage. Their props are usually less likely to snag a line, but they can't steer backwards.
Fin Keel boats have hulls shaped more like a u so they have less surface area underwater. The fin keel is usually shorter and deeper than a full keel and they are usually bolted to the hull or a keel stub. Fin Keeler's point higher into the wind and are faster but some can pound so heavily it will feel like the boat is falling apart. Their rudders are either skeg hung or mounted on a shaft through the hull with bearings. This design is the most prone to damage.
There are also modified full or fin keels like a Valiant, with a longer shorter but not full keel.