The debate has gone on for over a decade at this point: whether a fiber-based optical internet connection is best for gaming, or if linking up with ol’ fashioned copper is just as good. For almost half of the folks in the US, the argument may be meaningless, as they still can’t choose their internet service provider if they want a broadband connection (defined as a modest >25 Mbps download, and >3 Mbps upload, per the FCC). But at least in the most recent data, approximately 54 million US households did have a choice between two broadband providers, and a lucky 7 million actually had access to three providers.
On the cable side of things, we have an aging copper infrastructure based on coaxial wires and amplifiers to propagate the signal across distances, with the speed of data transmission through a copper wire being about two-thirds the speed of light in a vacuum. Cable throughput speeds have traditionally been lower than fiber options, although DOCSIS 3.0 enables 1 Gbps download speeds (but this is not a symmetrical connection as the upload speeds max out at 100 Mbps), and its followup standard DOCSIS 3.1 promises even faster 10 Gbps speeds. Both are still being deployed and are not fully available.
The optical fiber side is the newer technology, with the data carried via pulses of light through pipes made of glass. To avoid confusion, know that cable carriers these days have a fiber optic backbone, and use the coax for their ‘last mile solution,’ that is, the cable that actually reaches your residence, whereas ‘fiber internet’ means the fiber goes all the way to your residence.
While it would seem that data would travel faster through fiber, the refractive properties of the glass slow things down, and it really travels about 31% slower than through air, so the speed of these photons is quite comparable to electrons in a coax cable. There’s less need for amplifiers, though, as the data-carrying photons can propagate further than electrical-based connections that have to deal with the resistance of the wire.
While cable could catch up, fiber leapfrogged it and so generally offers faster speeds due to its more modern and recently deployed infrastructure. Some better ones, such as Google Fiber, offer a 1 Gbps symmetrical connection.
Looking at this question solely in terms of bandwidth, then, fiber connections are currently superior, as in most cases they offer a fatter pipe for download as well as uploads. As far as gaming goes, that simply means you’ll be able to download games faster.