TheSteamyPot has asked a question which reflects an age old debate.
Gaiwan or yixing for oolong is a complex question. This is a question for which I can not give you a precise answer because both are commonly used in oolong producing regions of China and Taiwan.
Think of the gaiwan not only as a cup with a lid, but also a porcelain or glass non-reactive device in which to prepare the tea. Similar, but not identical results to this method could be produced by a glass or porcelain teapot or infuser mug.
People in China and Taiwan also drink directly from gaiwans throughout the day by adding tea leaves of their choice in the morning and adding hot water to the leaves throughout the day producing many infusions without having clear 1st vs 2nd infusions to create a more continuous tea experience. This is good if you like tasting the tea as it changes and develops while not having precise control over temperature and timing. The lid is also a tool that can be used to help the leaves infuse fully and adjust temperature. Because gaiwans are made from a non-reactive porcelain or glass, they can be used for any tea. Porcelain and glass teaware of any type can be used for all teas to get good results.
Gaiwans are also used traditionally for the controlled tastings as the crops come in. Some farmers now use the more Western tasting sets. Tea is prepared in the gaiwan, decanted into a serving pitcher, and served in tiny tasting cups the size of golf balls.
Yixing pots are made with the rare purple sand clay. They absorb the flavor of the tea that they make because they are unglazed. The porous nature of the clay absorbs the flavors of the tea into the walls of the the pot. Originally developed with oolong teas in mind, but also used widely for puerh teas. After you make the same tea in the pot a thousand times or so, you should be able to pour water into your pot and make the same delicious tea. I have a small collection of Yixing with each pot devoted to a separate tea: one for green tikuanyins, dark roasted tikuanyin, baochong (aka pouchong), dark roasted high altitude Tung Ting teas, aged puerhs, and the list goes on. When properly prepared in a simple tea ceremony, the tea always seems to taste fuller, more complex, and puts me in the best mind frame to fully appreciate the tea. In some rural areas, men will drink directly from the spout of the teapot rather than use a gaiwan. I have not seem a woman drink in this manner.
Yixing teapots are very rarely used to prepare white, green or black teas while all teas can be prepared in a gaiwan or other glass or porcelain teaware.
While I love yixing for special occasions, I drink mainly from gaiwans and cups with infusers especially while working and reading in solitude.