In all fairness, it would be a shame not to use both of them - what I would say is that the first is more professional, whereas the second is more quirky, so it entirely depends on what you're going to use them for!
The first one is cleaner and easier to read. The 2nd is creative and innovative. Depends on the context of the site really, but as far as branding id say #2 and if you want ease of look and use go with #1 ! Sorry i couldnt be more decisive lol
As they are, 2 is more attractive, maybe the no.1 without the gray thing around the circle, and a darker gray.