I'm sure you must have gone through the net for both the technologies.
Both technologies provide integration, AOP and ease.
The major difference is Seam is more geared towards Stateful architecture while Spring is more suitable for Stateless.
Also the EJB3 support in Seam is a major reason to consider the framework.
Seam is based on EJB3 and JSF - the two technologies from Sun. And seam is also being promoted as Web-beans.
Each framework has its pro's and con's. You need to evaluate the framework based on your needs.
Comparing similar features offered (like remoting, persistence etc), my vote is for Seam. But if you want a wider integration with other frameworks and a better documentation it should be Spring (may be till Seam gets more documentation and how tos). But if you are not under pressure to meet a strict deadline Seam is the way to go.