Given that we're using digital sensors, in a high contrast situation, the thing to be careful of is highlights. Why? Welp, each photosensor (AKA 'pixel') measures, essentially, the number of photons. Once you go past 'full', there's no way to recover any overflow information.
On the other hand, the worst that happens with too-dark areas is that they can be overwhelmed with noise.
For film guys, think of digital sensors like transparency film (once the film is clear, there's nothing at all left).
Either way, the secret is to get as close to blowing out the highlights as you can - without actually blowing them out - so you're getting as much of the scene as possible to fit between 'almost blown out' (light) and 'too much noise' (dark)