There is a lot to unpack in your question.
1. Your Xfinity Cisco is combo unit that both the modem (required to get the signal from Xfinity) and the wifi router, that broadcasts the signal wirelessly from Xfinity.
So, on one-hand, No it won't replace, as this Linksys unit is only one piece of what is needed to broadcast wifi in a place, but you could add this to your system. There would then be two wireless signals being broadcast. I am not sure if your current equipment can have the wifi radio's turned off via the settings menu. Also, your are being charged a monthly fee for having Xfinity equipment, you could purchase a DOCIS 3.1 Modem and replace your equipment. They do make combo units like yours as well to purchase, but these units (sometimes also called a gateway) typically don't have the range as having a two-device setup: modem and router.
2. The speed you state of 15Mbps for internet is first determined by your Internet Plan with Xfinity. Changing equipment won't get you a faster initial download/upload speed outside of what your plans limitations are. Changing your equipment will give you better wifi coverage and determining on the equipment change, may allow your other devices to "talk" to one another faster which is not based on Internet bandwidth, but determined by the network equipment ( namely the router).
So to recap just purchasing a new wifi router won't give you faster download speeds if your plan with Xfinity limits it to 15Mbps. If your plan is rated higher than that and you are not getting close to the rate speeds, then yes changing equipment may be necessary. In which case, you can either A) request new equipment from Xfinity and may require tech to come out (can be free if there equipment you are paying for is faulty) or B) purchase your own equipment (Cable Modem and Wifi Router) and return your equipment stating you are not canceling service, just using your own equipment.