First, what PN do you have on the bottom of the modem? Does it have 4331 in it? If so, you have the CGM4331 gateway. It is a modem/router combo with public Hotspot wifi and phone. If you go with your own modem and router you lose the hotspot but you gain performance and flexibility. Some of the things which become problematic or impossible is port forwarding and alternate DNS. This makes things like camera, gaming, and parental controls difficult. If you have phone you can get a free phone modem(eMTA) like the TM3402. However the TM3402 doesn't have a 2.5Gbps port so you won't get above Gigabit speeds. If you have 2Gbps service plan, then the Arris TM9202 is a option. Either way you would still need to buy your own router.
As for "got-cha's" the main one is you don't get much Cox support unless your using their modem/gateway. It is also required to use Cox Homelife and wireless TV boxes.
