Some trivial some more involved:
* Your router won't have to work quite as hard with just routing the IPv6 connections compared with routing IPv4 and NATing them. i.e. performance per watt.
* Things like VoIP and some online games may be able to work a little more reliably when the source address and ports haven't been mangled on the way out.
This would really have helped older games where you can choose to host the multiplayer session and the lobby is on your device, more than the ones with a launcher and dependent on the vendor's own servers.
* If you are accessing a NAS remotely - hopefully by VPN though - you can specify that device to be reachable by selected parties without having to have them connect to the router, and without having to mess with the port numbers if you have more than one of a type of device
So say your had any number of web servers they could all be using port 443 for example and it won't try to load your router's web interface from the outside, all your phones can use port 5060 and so on.
* It becomes more practical to run a DMZ network because you can create additional subnets using addresses assigned to you (about 250 subnets on /56 or many more on a /48)
Or if you have reason to have another router layered inside your network it can request and automatically receive a pool of addresses to create one or more inner LAN subnets.
* Routers can actually handle more ongoing connections because it won't run out of source ports in the way it could with NAT.
This last one is less important unless you have > 1000 devices because that's a rule of thumb for how many you should place behind one public IP !
prlzx on Zen: FTTC (VDSL) at ~40Mbps / 10Mbps
with IP4/6 (no v6? - not true Internet)