I have used both. Bias warning: I use Altium (the full version) daily but do like many other PCB tools.
1.) Upverter is a brower based application and works on files in the cloud (I.E. google docs). At the time I evaluated the product, you need a persistent internet connection and it needs to be *fast*. I did a board design evaluation and it is extremely slow for anything non-trivial. Some browsers did a better job than others. The ability to cross platform is attractive but that is much lower of my list of needs. Performance and capabilities are my biggest requirements.
2.) CircuitMaker is not browser based. CircuitMaker runs locally on the machine and works on locally cached files. Project files are version controlled (SVN backbone) to the cloud. CM is essentially the Altium backend with a simpler GUI and the web/community backbone. It literally uses the same back-end .dlls, etc. It just has a simpler GUI with some of the advanced features (rigid-flex, etc) taken out. There are a few things I miss about the full version but still has more features than any other free tool. Internet connection is required to sign in to start and then when you need to commit. You otherwise are working locally so it is a hybrid of sorts.
The PCB editor is light years better in CM (push-shove, differential pair routing, real 3d, etc.). Upverter's PCB editor is similar to EAGLE (about 15 years behind everyone else) but with a better UI and a handful of extra features. It is still primitive though.
If you like the portability of a browser based app, Upverter is nice. The pricing of it is horrific for the limited capabilities of the tool though. If actually had to purchase it, you might as well buy a real tool (Altium, Orcad, Diptrace, etc).
The Schematic editor in CM allows for true hierarchical design. When I evaluated Upverter, it could not but may have since changed. (This is a big one for me!)
Both tools have risk. Upverter has yet to show a profitable model and has no other revenue stream and certainly could go away. CM is new but Altium as a company has a very large ($80mil) yearly revenue stream from their other products. It could always be pulled but they have invested quite a bit in it over the past 1.5 years and is starting to really shape up. The way CM is compiled makes it easy for them to pull in new features without maintaining a 100% separate product.
Bottom line: I have found the only way to evaluate a tool is to spend at least one non-trivial board design with it. That usually will narrow down your choices. Pick something and give both a try. Chances are you will find things you don't like about either but it will give you a taste.