The only thing that I think should be added is some more contrast but I wasn't sure, tell me what you think.
Definitely lose the border and the text, neither fits too well. It looks a bit over sharpened and LQ but everything is that way so I guess it fits. You need to add some contrast, like you said, and try and lose some of the brightness.
Version 2 defiantly much better, think the text needs to come closer to spidy though and maby a tad smaller