I am looking to upgrade my Wireless network. The house is large and I have an ASUS 3100. It doesn't reach well into other areas and we have a lot of wireless devices...Give or take we have between 20-30 devices at anytime connected to the wireless. Generally multiple TVs, xboxes, ipads, phones etc. Would it be better to install a mesh network like Amplifi HD Gaming model or add to the router using AiMesh from ASUS?
If you have the ability to run a AP that is your best option. Mesh is just a new marketing term for wireless repeater. Some work better than older repeaters but mostly it is a magic box for people that think you can solve wifi problem by plugging more boxes in.
All devices like that suffer from having multiple radio signals between the user and the router. It greatly increases you chance of getting interference. It is bad enough that people run game on a wifi connection directly to the router or a AP.
If you have ethernet cables to the remote rooms you do not need any form of mesh. Mesh almost always means wireless repeater. You can use pretty much any router running as a AP or you can buy real AP from a company like ubiquiti. It still is one network and all devices can communicate. This is nothing new AP have been used since the beginning of wifi mesh just pretends it is something new.