EJB's specification 1.x and 2.x added complexity that for most webapps was not needed.
Due this complexities the new frameworks appeared to simplify the development and the runtime architecture ( Hibernate / Spring / other microcontainers / others ORM frameworks ) .
EJB's 3.x matches this changes ( through JDO and JPA ) and now, using Servlets with these enhanced frameworks or Java EE with EJB 3 + would give you basically the same results.
Using a Java EE Application Server would add you a number of administrative advantages ( GUI to manage pools, logs, monitoring, transactions etc. ) With out them you may have the same result but you would have to do it all by hand ( editing configuration files that is ) Which may not seem too problematic, but if you plan to have an administrator for your webapp It would be better to use the admin tools that come out of the box with this servers.