Well both devices support QoS, but I would lean towards using the router. Why? With the router it seems you have much more capabilities for troubleshooting and figuring out what’s going on in a QoS scenario. A router for example supports NBAR and an ASA does not. The netflow logging is also different in an ASA as it’s not quite the same as a router. It uses someting called NSEL.

I think because QoS can be a trial and error process while you try and tweak it to work the best in your environment, it helps to have all the tools at your disposable and using a router seems to meet this goal. An ASA is great, but in my opinion is more security focused and not ideal in a scenario where you need full QoS capability.

-RP

This is all good and well until you are running a small business where every dollar counts. Luckily with the Cisco ASA you can implement web filtering without subscribing to a web blocking service. You can still subscribe to a service if you want to, but you aren’t forced to.

Instead you can use class-maps in the ASA to provide the ability to do this. This should only be done in small environments however. Once you go to a larger environment you should buy the subscription service. Please visit this link for instructions on how to do this.

-RP