Both options are the same in a way. If you use routers the recommend method is to use only the lan ports and disable the DHCP. It makes your "router" into a wireless switch/ap. It is mostly a cost thing. You can many times get a router for less than a AP. One of those strange things when it comes to pricing.
The key time you want to use AP is when you want/need to provide the power to the remote device over the ethernet cable. There are not a lot of PoE routers but almost all AP support PoE.
I have an existing network in a 300 year old structure. There is a base router from which there are 3 wired (ethernet) lines to parts of the structure. Due to the structure itself (near 2 ft thick walls - masonry) the wireless from the base router reaches only a short distance. I would like to "extend" the wireless reach using those 3 existing runs.
So - can I add 3 more routers or should I go with Wireless Access Points or what else would work?
Greatly appreciate the help! Chris