**Explanation:**

The correct answer is option B - "While he was holding the old vase, he dropped it."

Here is the detailed explanation:

1. **Simple Past vs. Past Continuous tense:** The difference between option A and option B lies in the verb tense used in the sentence. Option A uses the simple past tense ("held"), while option B uses the past continuous tense ("was holding").

2. **Past Continuous tense:** The past continuous tense is used to describe an ongoing action that was happening at a specific moment in the past. In this case, the action of "holding the old vase" was ongoing when the person dropped it.

3. **Context and coherence:** In order to provide a clear and coherent sentence, it is important to use the appropriate verb tense that accurately reflects the sequence of events.

4. **Cause and effect:** In this sentence, the dropping of the vase is the effect, and the action of holding the vase is the cause. It is logical to use the past continuous tense to describe the cause of the event, as it emphasizes the ongoing nature of the action.

5. **Clarity and understanding:** Option B provides a clearer and more concise description of the situation. It clearly conveys that the person was in the process of holding the vase when they dropped it. Option A, on the other hand, may create confusion or ambiguity about the sequence of events.

In conclusion, option B - "While he was holding the old vase, he dropped it" - is the correct sentence as it accurately conveys the ongoing action of holding the vase at the moment of dropping it.