Multi-Armed Bandit and A/B Testing are two popular methods for optimizing user experience in areas like website design, marketing strategy, or policymaking. 

A/B Testing involves comparing two alternatives, whereas Multi-Armed Bandit progressively allocates more resources to the best-performing option. Understanding when to use one over the other can be a game-changer.

Simplified Explanations

A/B Testing: 

Think of it as a school test. Half of the students study Method A, the other half study Method B. At the end of the experiment, we see which group has performed better. The main advantage of A/B Testing is its simplicity and comprehensibility. Some drawbacks are requiring a lot of data and may miss temporary trends due to its static nature.

Multi-Armed Bandit:

In contrast, it's more like training a sports team. All team members start training with the same intensity. As soon as one shows better results, more training is assigned to him/her. This approach is more efficient, especially when you need quick results.

When to Use A/B Testing

• Use it when you have plenty of time to gather and analyze data;
• If you're assessing options that are unlikely to change over time, A/B Testing is appropriate as it's more static;
• Use it where clear-cut answers are needed- whether option A or B is more effective.

When to Use Multi-Armed Bandit

• Use it when you have multiple alternatives and limited time or resources to explore them;
• When your environment is dynamic, like in online advertising where trends change rapidly;
• If you're accepting some degree of uncertainty for the sake of fast results, go for Multi-Armed Bandit.

Combining Both Methods

Is one approach better than the other? Not necessarily. In many situations, a blended approach is beneficial, beginning the testing using A/B Testing's simplicity and clarity then transitioning into Multi-Armed Bandit's efficiency once initial data is collected.

To summarize, choose the method that best suits your specific situation: consider factors like the nature of your options, the speed of results, your available resources, and the amount of risk you can tolerate. Both A/B Testing and Multi-Armed Bandit provide effective ways of optimization, but their applicability depends on case-by-case scenarios.

Remember, these techniques are tools to aid you in your decision-making process. Always complement these with sound judgment and good old-fashioned common sense. Happy testing!