In most case I would say it is all in your mind. But many first person shooter guys think they were born on krypton and better eyes and reflexes than all the other measly humans.
Going from say cable to fiber might cut your latency 5-10ms but that doesn't matter since games are designed to not give someone who has lower latency a advantage. If you dropped it 100ms then it would make a difference.
Going from 1 fiber plan to another fiber plan will be identical. The data rate limitation is artificial. The data between your house and the ISP router is always at the very maximum rate. Most systems use GPON which runs at 2.5gbit. So no matter what plan you pick you data always leaves your house at 2.5gbit.
If you were to download large files the ISP will cap your rate at 100mbps BUT the data still transfers at 2.5gbit. What you see is a average rate.
If we take the case of say ethernet which also always runs at 1gbit as a example. Lets say you put a QoS limit in your router of 100mbps. As a example your pc would transfer data at 1gbit for 1 second and then do nothing for 9 seconds. It would get a average rate of 100mbps. You get the same average if you were to transmit data for 1/10 of a second at 1gbit and then do nothing for 9/10 of a second it is still a average rate of 100mbps.
So it doesn't matter which plan you pick it is a artificial limitation your data is actually running at 2.5g or whatever fiber standard your ISP is using.