You didn't mention what type of hob, but if it's a gas hob, I would definitely be looking at external extraction, as there's all sorts of combustion gases that won't get filtered out, and aren't very good for you.
But for electric or induction hobs, recirculating hoods are very common, and most people seem to get on fine with them.
Exceptions would be if you regularly cook foods at high temperature that produce smoke, or cook things that produce a lot of steam like a simmering stew.