One of the biggest differences between wood and fiberglass drums is that fiberglass tends to have a louder and crisper sound. Basically it's a bit more resonant; whereas the wood is warmer and more natural sounding. The louder and crisper sound can be good for cutting through the mix of an amplified band, however might not produce that warmth needed in a studio recording environment. Since the fiberglass is a little more resonant it's slightly easier to produce the tones, which can be a positive for those just starting out because of ease of play. I would argue to say that most professional players choose wood due to its warm and natural sounding tone. Plus wood congas are much more authentic and traditional. Fiberglass congas will be less affected by changes of weather and temperature although they tend to be heavier than wood drums. The wood responds more to atmospheric changes, but since they are tunable that may not matter too much.
If you're planning on gigging out a bunch and transporting your drums around town, keep in mind that wood tends to show scratches more easily, though both are very durable. A drum usually gets most of its scratches when traveling, so if it's mostly kept inside then you reduce the chance of damage.