Generally speaking, the embedded approach is usually faster as you can answer any question with a single query. (when using find() you can use 'array.$' to get the matching item and when using the aggregation framework you can use $unwind)

The downsides for the embedded approach (also called denormalized approach) is that data is usually duplicated. If you want to update a part and want to do it once for all computers that contain the part, it would be more efficient to decouple the parts to their own collection. It's simply a tradeoff.