Charcoal isn't as bad as wood, it creates less smoke and the most complex chemicals are already gone. Gas is better, since it burns much cleaner, and electric obviously doesn't create any gasses at all.

On the other hand, grilling and smoking red meat means dripping fat, which means smoke, meaning you create a whole new set of PAHs (polycyclic aromatic hydrocarbons), which you breathe in and get stuck to the meat and those are carcinogens. On top of that, red meat is already not too great for you. Eating burned food (charring) is also really unhealthy.

But assuming you don't spend every day breathing mostly bbq-smoke and gasses, I wouldn't worry about this too much. If your main diet is home grilled beef over self-made charcoal, you definitely need to reevaluate your lifestyle choices though.