It's a matter of preference, but if you're getting TV service as well, I would advise just sticking to Coax only.
There are actually several networks working together when you get FiOS internet and TV service.
1. The ONT to the STB's provides QAM signals for the TV channels which are decrypted by the STB. So, for this you need Coax from the ONT to each STB.
2. The Internet service can be provisioned to the router either via Ethernet or MoCA Coax. They are essentially equivalent in functionality, it's just the media which is used which is different. Since coax is a broadband capable medium, there can be many different transmissions occurring simultaneously on the same wire without them impacting one another (essentially, MoCA WAN runs on a frequency of 1000Mhz and I believe most QAM runs in the 6Mhz band).
3. The STB's need access to the internet in order to get their guide data, VOD, etc. This is accomplished using a MoCA LAN connection channel between the STB's and the router. The MoCA LAN runs on 1150Mhz.
The router bridges together the local ethernet ports on the router, the wireless network, and the MoCA LAN connection to form one logical network and then processes the traffic thru the NAT/PAT Firewall engine to either the MoCA WAN interface or the Ethernet WAN interface depending on how your internet traffic is configured.
In short, if you go with ethernet for the WAN to ONT connection, you'll still need a Coax connection into your router so that the STB's can get to the Internet. Your only real benefit of using an Ethernet WAN interface connection comes if you are not a TV subscriber and wish to use your own residential router (most residential routers are much simpler to configure than the Verizon supplied router which is necessarily more complex due to the functionality which is supports).
It's important to note that you can't use your own router with a WAN Ethernet connection in place of the Verizon router if you have TV service if you want everything to work properly (the router assigns specific addresses and quality of service attributes to the STB's so that they function properly and the Verizon central network looks to be able to communicate directly with the Verizon supplied router to make necessary configuration changes for things like Remote DVR service which will fail if you substitute a different router (OK, "can't" is too strong a word -- it is possible, but unless you truly understand how networking and routing works and what is going on under the covers -- you should not be exploring that territory).
