The manager of component 'A' says his functionality is more important than that of component 'B.' The manager of component 'B' says his is more important than that of component 'A.' You can only implement one A or B, but not both - which do you choose to implement.

The key question to ask is definition of "IMPORTANT". Is it important to the managers (ego equation), important to the end consumer or important for Amazon. The first one needs to be thrown out immediately and the others must be quantified based on achievability, impact on end user and ROI.

I would say whichever is more valuable to customer & gives competitive advantage to Amazon.

Agreed. Need to drill into what "important" means. Great catch My guess is that Amazon was looking to quantify/define "important" from the customer perspective.

In addition to the above suggestions, I would look at cost and time to market and then score both options. Then define value metrics. The cheapest and most valuable either as a technology sustainer or for customer wins. Given that it's Amazon, customer value will hold up the highest as one of their corporate culture virtues.

I would recommend doing a data collection plan on the "functionality" - can you quantify the functionality and its execution be turned into hours saved, steps minimized, bottlenecks reduced, inefficiencies gained?

How was "important" defined and what data backs up the claim? What is the impact of selecting component A v. B on budget, time to market, feature creep, deadlines, etc. Another key data point is what is the risk of selecting one over the other? Are both important enough to change the release plan, or can one be added later as a product improvement?

I would use the RICE Analysis for both the feature in this case, R - Reach, how many people this feature effect? I - Impact, How much does this feature impact, individual users, e.g massive, high, medium, low, minimal, etc C - Confidence, How confident are we about the impact and reach scores? E - Effort, How much time, the investment will this initiative require from product design and development? (Reach X Impact X Confidence)/Effort = Rice Score Other Prioritization methods can also be used based on the information I will get during the interview, like MoSCow analysis, WSJF, Kano analysis, etc

Each organization follows different strategy and long/short term goals. At the same time they also do have different principles. Amazon is the most customer centric company. So if I assume the manager if from amazon, they need to look towards more customer success in both plan A and plan B. Couple of other factors also need to be quantitatively calculated to take the better decision.

NPV should be calculated for both projects. Whichever project has higher NPV than IRR should be selected. If both project has higher NPV than IRR then higher NPV value project should be selected to proceed.

I would recommend doing a data collection plan on the "functionality" - can you quantify the functionality and its execution be turned into hours saved, steps minimized, bottlenecks reduced, inefficiencies gained?

I would collect data and take the decision. Type of data that you need collect depends on functionalities.

I would say to do my own research

This must be escalated to the program management team or a higher authority to make a decision. This decision should not be made at the level of a product management.