(This'll probably need help from someone more specialized in the network side of things)
Internet performance is great, other than when playing a specific online game. FFXIV: A Realm Reborn. I've looked into this and have seen that a lot of FiOS users have the same issue with this same game. Its commonly blamed on the routing path the network has to take to get to the servers for that game.
I only switched to Verizon a couple weeks ago, and previously had Comcast. This issue didn't exist with Comcast, so I doubt its a problem with the game's servers. Its commonly blamed on a poor routing path that Verizon provides to their servers.
Here's a trace route to their servers.
C:\WINDOWS\system32>tracert 199.91.189.27
Tracing route to 199.91.189.27 over a maximum of 30 hops
1 <1 ms <1 ms <1 ms FIOS_Quantum_Gateway.fios-router.home [192.168.1.1]
2 3 ms 1 ms 1 ms L100.PHLAPA-VFTTP-84.verizon-gni.net [98.114.194.1]
3 4 ms 7 ms 7 ms G0-13-1-3.PHLAPA-LCR-22.verizon-gni.net [130.81.212.222]
4 * * * Request timed out.
5 * * * Request timed out.
6 8 ms 8 ms 8 ms 0.ae2.BR1.IAD8.ALTER.NET [140.222.229.165]
7 8 ms 8 ms 8 ms te0-6-0-14.ccr41.iad02.atlas.cogentco.com [154.54.10.225]
8 9 ms 10 ms 8 ms be2171.ccr41.dca01.atlas.cogentco.com [154.54.31.105]
9 16 ms 16 ms 15 ms be2148.ccr41.jfk02.atlas.cogentco.com [154.54.31.118]
10 20 ms 19 ms 19 ms be2106.ccr21.alb02.atlas.cogentco.com [154.54.3.50]
11 24 ms 24 ms 24 ms be2088.ccr21.ymq02.atlas.cogentco.com [154.54.43.17]
12 35 ms 36 ms 36 ms 38.122.42.34
13 47 ms 50 ms 49 ms 192.34.76.10
14 48 ms 48 ms 48 ms 199.91.189.242
15 48 ms 49 ms 49 ms 199.91.189.27