For the LAN, faster local transfer if you use huge file or if you have a lot of computers accessing your server.
It's also useful if you live in Europe since a lot of country has 10Gbps as long as you have access to fiber since half a decade now (the krone world wide being Switzerland with a 25Gbps home offer on dedicated fiber).
In your case, router will be the bottleneck so not worth as long as the router isn't upgraded, you're always tied to the slowest part.
The non-chromium based browser are: