What does it mean for one language feature to be more powerful than another?

When reading about programming languages, especially discussions involving Lisp, the word "powerful" seems to be used to describe certain languages or features (you'll hear about Lisp's macros being called "powerful" all the time). This wording should cause for immediate question for those who don't know the definition of "power" that is implied here. It is well known that all Turing Complete languages actually have the same power. Since this is true, that raises the question: what do people mean when they say a language feature is more powerful than another?

The most common example of talk can be seen with lisp macros. You'll see questions like this one or here and people asking "Why is Lisp called the most powerful language" . That last link has many answers on Quora suggesting different reasons why Lisp is deemed so powerful. One of which claims that "powerful" is an actual term which means "you can do more with the [Turing-complete] language in a finite amount of time". This, like the other made up definitions is flawed. This example cannot be true because

People should stop using the word "power" to describe the expressiveness of a language. This leads to misconceptions about languages and often puts more logs on the flame wars between languages. The words "lisp macros are the most powerful" is now forever in my memory from the number of times I've read that phrase. I agree of the opinion that lisp macros are the most expressive language feature, but to say powerful is misleading.