When people this about the concept of beauty, most cases are descriptions of a look. Outward appearance. The well maintained and manicured nature of a person's hair, makeup, nails, and clothing. Those who have been challenged to look deeper than surface beauty, would argue that the "beauty" of a person can be found in their character, their grace, quality relationship, and skillset they leverage to navigate through life.
I'd like to think of beauty as a candle. I know it sounds so weird to describe it like that. But when you look at a candle, they come in different shapes, sizes, colors, and made of different materials. They are all provide similar things. First and foremost; light, then others provide fragrance, some for just the purpose of a pleasant scent and others for to change the comfort level of their environment (OFF!) Before you even attempt to light the wick, it is filled with the potential of providing all these things, when it was crafted; whether by a machine or by hand. No matter the material; soy, traditional wax, bee's wax, paraffin wax, palm wax, or any other kind, they all surround a piece of string, that will at some point, burn away to get to the real of what it is designed to do.
In this analogy the string represents the inner beauty of a person; their character, heart, kindness, passion, and love for life, etc; where the wax is just the casing that intrigues people to want to come closer and discovery more. While the inner beauty is great to have, the outer beauty is what captures your audience and invites them to want to find out more about you.
Is one more important than the other? Where should you concentrate your efforts? What does the word say about this topic? From a biblical perspective "Charm is deceptive, and beauty does not last; but a woman who fears the lord will be greatly praised" -Proverbs 31:30. To me this notes that both should be considered, but are not nearly as important as the spirit.