Full frame is generally accepted as the standard format for most professional work and is what most photographers would choose if given the option. However, that does not mean that full frame is the best choice for everyone nor that you should spend extra money for it, and this fantastic video details several reasons why.
Coming to you from Robin Wong, this great video features him discussing a few reasons why he does not shoot with a full frame camera. No doubt, full frame sensors give a fair number of advantages, including great control over depth of field, better low-light performance (all other factors equal), and more, but they also come with a variety of disadvantages, or sometimes, depending on your needs, the advantages simply are not that relevant. The first is the simple bulk; full frame sensors generally demand bigger and heavier bodies and lenses. Second is cost: full frame bodies are often pricier, but even more notable is that full frame lenses tend to be more expensive as well, and those costs can add up quickly. If you do not the bleeding edge of noise performance or ultra-narrow depth of field, you might actually be better served by something like Fujifilm's popular X Series. Check out the video above for the full rundown from Wong.