Brick readily conforms to any curves or angles you wish to apply, as well as a great number of patterns. Wood decks are generally quite linear, running the length of the boards. Changing the direction of the run, however, can easily break up long, straight lines. Decks go down relatively quickly. And, of course, if you are building several feet off the ground, a deck is vastly easier than trying to construct a support system for a brick patio.
Wood decks require some maintenance, such as sealing, cleaning, and repairs to damaged wood.
Both brick and wood can be slippery and mossy in wet, damp areas. They are not sold to the public, but only to licensees of the maker, Bomanite Co. Retaining walls can be built out of almost anything, including bricks, fancy interlocking blocks, field rocks, old railroad ties, or even broken pieces of concrete. What material you choose reflects how formal or informal you want it to be. If the wall is going to be higher than 4 feet, you should get professional advice because you do not want it collapsing on someone.