Let's quantify this... what do we mean by better, because I don't think any of us mean more innately valuable. At least for me I would measure this by the diversity and accuracy of ability based on the experience of life. To gain ability you must learn, and not everyone chooses to. That choice may not seem available when overwhelmed, but its there.
To that extent, the level of affluence in your life is immaterial compared to the level of allowed comfort. You can be comfortable sitting in a crummy rental house smoking weed with your friends from high school and you can be comfortable in your mansion in Beverly Hills. Comfort is the absense of stress. Its valuable in the same way that sleep is. It allows you to process your experiences in the hopes of increasing your capabilities, but stress is what creates those valuable experiences.
A rich kid could be presented with a menagerie of learning experiences if they're not coddled or spoiled. Imagine the world traveling and the classes from very well put together people. A poor kid may not have those opportunities, but they have the potential to understand basic human need and the immobilizing force of despair on a sociological scale.
I've toyed with the idea of raising my potential future kids in a religious atmosphere, just so they can gain the invaluable perspective of someone who has had to retool their worldview from what was first presented to them as children. The ability to see how even you might feel certain about something one moment, and completely against the next creates the potential for understanding those your disagree with. Of course I wouldn't go through with it, but the concept is intriguing.
I think when most of us think about this we think of two people. The one who worked their way out of the ghetto, and the spoiled adult-child with a trust fund and a dearth of real compassion for their fellow human being. The word for the difference between them is "character" and we've heard it so much we tune it out. Someone with character is someone who when presented with something personally difficult (change in world view, physical task believed beyond their abilities, etc) they do it anyway, and they can do that because they're believe they'll be a stronger person at the end of the task than they are now.