Do you see how the old version is spaced so that it looks almost like a monospaced typeface? The letters all feel stilted and separate as if they don't like each other very much. The new letters by comparison flow into one another and feel more united as a word. The kerning isn't perfect on the new one, but it is better.

Ok, that I can perfectly see; the letters are standing tall, almost proud, separate to each other in the previous version.

When we talk about balancing the inner space of the letters with the space between letters, we're talking about total area, really, and not about just the optical width of the spaces, right? So that, for instance, if we take the “u” in the previous version: if we measured both the area of the spaces before and after it and the area of its inner space, we'd find out that there’s (a lot?) more space around the letter than inside it; whereas if we do the same thing with the new version, the numbers are probably a lot closer, even though optically it seems to have much more space inside it than outside.

Is this correct? It seems obvious and I've known this for quite a while, but I still can't “see it”, intuitively look at it and know it’s not balanced.

You don't always have the opportunity to see kerning upside down, but I've learned its a basic way to see the letterspacing with sort of new eyes. You're no longer seeing a word but instead the shapes and their spatial relationship with each other.