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Both are quite safe, because scientists have done multiple calculations to make sure there is no danger. The main difference is that liquid fuel - used primarily in jets - is more easily controlled, as you can turn on or shut off the flow, while the solid fuel - like in rockets - is going to be used up in one go, with less ability to control it. We don't tend to need the on/off capability in rockets, because we want the astronauts pushed into space, which is one straight sprint upwards.

You can say that, due to its ease of use, the liquid fuel is safer; but in both cases, the risk is minimal when the engine is properly designed.