Nowadays IOS router has a lot of the firewall functionality, however, configuring the FW feature on IOS router can be quite complex comparatively to a dedicated firewall.
IOS router would have more advanced feature on routing protocols, while compared to FW which has limited feature on routing protocols. When comparing firewall feature sets, ASA would be more superior. You can also have extra IPS module or CSC module to ASA firewall.
All in all, the complexity of configuring IOS FW has normally made people choose ASA firewall over IOS router as a firewall device.
FW and VPN throughput would normally be better on ASA compared to when you are running it on IOS router.
Comparing PIX firewall and ASA firewall, PIX is the older model of Cisco firewall, and has reached it's EOL. The replacement for PIX firewall is ASA firewall.
Hope that helps.