why such a discrepancy? Which site is the most accurate?
There are many variables which effect your ultimate download speed, such as the type and kind of cable used (if wired), the distance from the modem or router (if wireless), additional local activity on your network and numerous other temporary conditions. Unless yours is a fiber connection, you shouldn't expect consistent download results. It's just the way things are.
You may no doubt be aware of one or two sites where you can test your speed. You may also know from experience that even speed tests performed in rapid succession will yield varying results.
Cox offers two sites to monitor your internet speed. One of them https://www.cox.com/internet/speedcheck.cox requires that the computer used for the test has Adobe Flash installed on it. A different Cox site https://www.cox.com/residential/support/internet/speedtest.html is one which does *not* require Adobe Flash to be installed on the testing computer. I personally use Ookla's http://www.speedtest.net, mostly for vanity reasons, as the results are typically more in line to what you think you're paying for with Cox. Yet another reputable test site is https://www.dslreports.com/speedtest. I should add that neither of the last two recommended sites requires Adobe Flash to be installed on the testing computer.
I have recently been informed here on the Cox internet forum that logging on to your Cox account and using either of their speed tests *should* log the results of that test directly to your Cox account. That's the good news. The not-so-good news is that 1) Cox' test sites will typically result in significantly lower speeds than your current subscription tier, and 2) unless vigilantly and repeatedly followed up by you, the user, inadequate or less-than-favorable speed test results will not in and of themselves amount to anything other than customer dissatisfaction.