First of all JBoss AS is based on JBoss web for which the core functionality is provided by Tomcat. So the right comparsion should be JBoss Web vs Tomcat.
[JBoss AS] is a full fledged application server complying to Java EE6 Web Profile and with many modules. The JBoss AS 7 standalone configuration directory [//standalone/configuration] has 3 configurations available to use such as standalone.xml which is supposed to be a typical configuration, standalone-full.xml which enables all modules and a standalone-ha.xml which is for High availability. JBoss AS also supports a domain mode which makes multiple servers manageable from a single interface. So if you are looking for a high availability(optional) enterprise class solution, go with JBoss AS.
If you are not using EJB, your webapp can easily can easily run on Tomcat for that. Since you are planning to use Spring, I presume you will be using Spring to manage the lifecycle of components. So that means you will not use JBoss for lifecycle management. Also JAX-RS libraries like Resteasy have spring integration so you will interact with these libraries via Spring. The same thing applies for JAX-WS libraries as well.
I have seen several projects support both of them. The right comparison should be JBoss AS vs Apache TomEE.