If you are looking solely at oxygen production, you need to look larger than the scale of an individual tree, and look at the whole ecosystem. Yes, each tree produces oxygen, but each year, when the trees leaves fall, and when the trees' seeds are eaten by animals, and when trees die, and the dead wood and leaves decompose, oxygen is turned back into carbon dioxide. In many mature ecosystems, there is very little net release of oxygen--oxygen is generally being released (and carbon stored) fastest in a new, growing ecosystem, such as when trees grow up in a grassy field.
There is, however, an important distinction between northern boreal forests (where most plants are evergreen), and temperate deciduous forests. In a boreal forest, the temperatures are so cold, and the leaf little (i.e. the needles) is so acidic (low nitrogen content) that it doesn't break down much. Thus, it accumulates over time, and carbon is stored. In a temperate forest, the leaf litter is rich in nitrogen, and the temperatures are warmer, so the material breaks down faster.
There is an interesting exception to this--note, I mentioned that acidity and nitrogen content is important. In a bog, there is a very low nitrogen content, and thus the leaf litter becomes very acidic. Bogs also contain plants like Sphagnum moss which contribute to this acidic environment--they thrive in it so they make the environment more acidic so other plants can't survive. In this environment, stuff doesn't break down. The layers just accumulate.
This is how fossil fuels are made. In fact, you can even take the peat out of bogs and burn it for fuel--it's very dirty, however, although people have done this in poor areas of Great Britain at various points in history.
So...if you really want to think about net oxygen production, start thinking about ecosystems as a whole. And start thinking boreal forests and bogs, and also think about reforesting deforested areas. This is where the biggest CO2 storage impact is!