I have one of those 2010s myself and prefer it. I saw the new ones in the Apple store recently and they sure are pretty, but the 2010 has more usable functionality and is easier to upgrade. Besides I could care less about how thin the edge of a desktop computer can be. Looking at the 2010 or 2013 head on (which is what we will all do the vast majority of the time we own either), the thin edge is irrelevant at best (why did that SD card reader move around to the back again???).
Apple has done a great job on making some of the masses believe that ever-thinner is some kind of major benefit- even when to achieve that thinness, Apple must remove hardware utility and/or shift that utility to separate accessories. I suppose eventually all Apple gear will be as thin as a single sheet of paper, at which point the focus could perhaps shift to other targets that actually make newer models do more than older models (not just a little faster or via accessory attachments). Frankly, in my own case, I could almost care less how good (or thin or fat) my Mac looks as opposed to how well it helps me do what I need done.
The 2010 model also still runs Snow Leopard which is a bridge back to any legacy software dependent on Rosetta while the 2013 model pretty much put legacy software out of its misery. There's pros & cons in moving on, but the leanings are entirely in the subjective: if you need something that runs on Rosetta, you need Rosetta. If an upgrade is not available, the older SL-capable Macs are THE way to go. I have a few crucial applications that require Rosetta (no upgrades available), so I appreciate being able to still use those programs.
I hope that someone at Apple will eventually decide that how pretty the case looks is only important to the aesthetics crowd or the first impression "grab". It's the invisible engine inside that is much of what drives the lasting experience for Mac buyers. Sure, we want good-looking computing devices... but not to the point (IMO) where we overly sacrifice the muscle to squeeze a few more millimeters out of the shell. I want Macs that help me get more things done, not something to enter in "who has the thinnest desktop?" contests.