As phatch explained, baking powder and yeast are very different, even though they are both used to make dough rise. They give the doughs very different textures, and you cannot substitute one for the other.
Baking powder makes dough or batter rise through a chemical reaction: as phatch noted, first when the powder becomes wet, and then when it is heated. The reaction is the release of carbon dioxide gas (CO2) -- the two parts of baking powder are acid and alkali, and when liquid is added, they mix to form CO2. Then the heat in the oven makes the gas expand, and the bread or cake rises. One way you can tell if your baking powder is still good is to mix some with plain water: if it doesn't bubble some, throw it out -- it's too old and your cake or bread will be flat and horrible.
(One of the parts of baking powder is bicarbonate of soda -- also known as "baking soda." If that's the only thing you have, you must add some kind of acid in order to make it work. Acids that we use include buttermilk, lemon juice, honey, molasses. I hope this little aside isn't too confusing. )
Phatch said that yeast is alive. Yes, it is a tiny, tiny living plant. When you give it water and food (usually sugar and/or flour), it eats. Then just like us, it excretes the waste. Although in the case of yeast, what it excretes is edible gas, which stretches the strands of protein (gluten) in the dough to make the dough rise. In the oven, again, heat makes the gas expand. But it also kills off the yeast, so you don't have an oven filled with ever-growing dough.
suzanne is awesome i have replied to three posts and she is right there with great info and a ton of what i can only guess is "well earned experience"................... anyway in response to you question yeast offers the best end product by far... baking soda with some cream of tartar or other acid (ie baking powder) will give you good results for "quick breads" these are baked goods that do not sit around long like buiscuts, you mix them, roll them, cut them, and bake them. the reason for this is that the baking powder uses the liquid in your recipe as a medium for a chemical reaction. this reaction happens imediately after the the liquid comes in contact with the baking powder. there are other products as well like bakers ammonia, this is usualy only used in huge scale baking and results in an inferior product. with all that said yeast yeald the best bread. because it lives (feeds, grows,reproduces, and dies) it creates biproducts or waste the co2 which is what leavens your bread is one of the wastes produced by the yeast, the other, my favorite is alcohol. this alcohol if given the right amount of time will result in the fermentation of your dough. this greatly enhances the flavor. sourdough is a perfect example of this. i hope that what i have typed is of some assistance with your future leavening needs. keep the questions coming i liked answering this one .