While most of your comments that I have read before are easily understandable and well-thought I out, I don't what you mean by depth.
If it refers to color, the Sony images look like a Velvia-simulation in some LR plugin. One of the things that is really cool about Foveon color on the Sigma is that it captures both dull and lively colors with equal 'presence' in the same frame.
On the other hand, if depth refers to resolution and microcontrast, it sounds like your comments about the city would suggest a marked advantage for the Sigma. I did pay attention to the city, and I thought how muddy it looks in the Sony image. Then my gaze travelled over to Mt. Fuji, and the difference was compelling. The Sony is hazy placeholder on the horizon, the Sigma is living breathing mountain that towers over and away from the city.
To tell the truth, when I first opened the website, I thought for sure that the Sigma image, which has higher resolution, finer detail, and to my eyes better color, was from the the Sony (such was the hype around that camera's 36mp sensor).