An excellent article by Tyler Jewell which explains the differences between the J2EE Connector Architecture and Web Services with respect to Enterprise Application Integration. I get asked this question a lot myself, and generally reply the same way Tyler has in this article.
The primary difference is that J2EE Connectors provide tighter integration with higher qualities of service (QoS). Web services are much looser and provide weaker QoS (i.e. transactions, security, etc.), but Web services are great when integrating across platforms (programming languages and operation systems). From a J2EE perspective, using these technologies in combination is optimal.