CHEMEX belongs to the pour-over family: hot water is poured onto coffee held in a filter, and brewed coffee drains into the vessel below. Comparing CHEMEX with pour-over as if they were opposing methods obscures the real buying decisions. Filter construction, brewer shape, capacity and the serving routine are more informative points of comparison.
Consider whether you want an integrated glass carafe or a dripper that can sit on a separate cup or server. Check that the correct filters are easy to obtain, and account for the scale, kettle and grinder in your setup. A larger brewer is useful only if its normal dose and serving capacity match the coffee you make. Glass handling and access for cleaning also affect day-to-day convenience.
When comparing the cup, keep coffee, water and brew ratio as consistent as practical, then adjust each brewer's grind and pouring recipe deliberately. A slower drawdown does not automatically mean better flavor, and a single water temperature is not a rule for every pour-over tradition. Record the final recipe and judge the coffee rather than repeating unsupported claims that one vessel universally extracts more desirable flavor.

The conversation
A good question can make a better brew.