There ARE issues with Macs opening some bookmarks. It mainly seems to be https:// links. I can open a bookmark I dropped on my desktop and renamed from Cox.webloc to Cox just fine in Firefox, but if I try it in Safari, I get a blank screen. I don't use Safari because I think it's a horrible browser (although I think it beats IE and Chrome hands down, more below on that) but if I rename the bookmark to Cox.webloc, it opens fine in Safari.
Make a bookmark IN Safari for https://ww2.cox.com/resaccount/home.cox and you shouldn't have any more problems on your Mac.
That said, I've noted multiple times in the last 2 weeks that Cox just wouldn't load in any browser, but that appeared to be more of a website issue not the browser not working.The down times seem to be later at night, I haven't seen issues in the daytime at all.
The issues you're experiencing are not a Cox issue from what I can see, they are some issue on the Mac with the way sites open.
The other thing is, I've seen MANY issues with Chrome and IE (I work in the internet business) not loading some scripts properly. In fact, I see problems nearly every day with people using Chrome and IE loading some websites or particular pages on a website. I have them change to Firefox and the problems disappear and the page they are trying to go to loads fine. Whether it's a PC or a Mac, I've seen enough issues with Chrome and IE from an "outsider-looking-in" perspective that I think they both blow and you should try Firefox. Also, if you still have issues in Firefox, you can try loading a New Private Window that eliminates any extra garbage the browser is running (saving history, addons etc) by hitting Shift-Command-P. That will get a window to load on an ornery site sometimes.