AP's allow for more flexibility and accessibility as well.
If you are using a Wireless ROTUER, behind a WIRED router, both will be using NAT, which amsquarades one public(internet) IP into quite a few private IPs.
The problem arises when you want to route traffic a machine behind the wireless, or second, router. Thses" Simple" devices to not allow for inter-VLAN, or subnet, communication....
What does that mean?
IDEALY:Assuming you want to setup an FTP server behind the second router, you would start by fowarding the public port 21(or whatever) to the private port, which is the second router. Then the second router would be set to do the same to the FTP server behind it. Unfortunately, it sounds simple, however, these devices do not allow for traffic to traverse the networks in that fashion. This is one of the benefits of higher grade equipment for business-equipment.
APs, since they do not constitute a new network/subnet/VLAN, allow for direct communication to the router without a prohibitive intermediatary...just like cables