This has been happening since March. It has escalated. Now I can only log in and look at my own already uploaded files as if I'm a spectator at a museum. This bug has been reported by others but evidently Dropbox is not working on it? And no I dont' want to discard my browser/computer/anything just for dropbox. It's all working fine on all other websites and services.
Have you made sure both of the browsers are updated?
Also, I would suggest that you restore your browser to its default settings and disable any browser plugins. The issue you're experiencing may be the result of a security setting or a plugin that you have installed on your browser.