I am facing a typical situation where one node is running fine while in another node I am getting the below mentioned exception:-

I am using hibernate 3.0.3 version along with struts2-core-2.3.20.jar

[12/18/15 5:33:51:883 CST] 0000001f webapp E com.ibm.ws.webcontainer.webapp.WebApp logError SRVE0293E: [Servlet Error]-[org.hibernate.impl.SessionFactoryImpl (initialization failure)]: java.lang.NoClassDefFoundError: org.hibernate.impl.SessionFactoryImpl (initialization failure)
at java.lang.J9VMInternals.initialize(J9VMInternals.java:140)
at org.hibernate.cfg.Configuration.buildSessionFactory(Configuration.java:1055)
at com.citigroup.rel.citiworks.util.HibernateUtil.<init>(HibernateUtil.java:66)
at com.citigroup.rel.citiworks.util.HibernateUtil.getInstance(HibernateUtil.java:38)
at com.citigroup.rel.citiworks.login.LoginFilter.checkUserChannel(LoginFilter.java:90)
at com.citigroup.rel.citiworks.login.LoginFilter.intercept(LoginFilter.java:245)
at com.opensymphony.xwork2.DefaultActionInvocation.invoke(DefaultActionInvocation.java:244)
at org.apache.struts2.impl.StrutsActionProxy.execute(StrutsActionProxy.java:54)
at org.apache.struts2.dispatcher.Dispatcher.serviceAction(Dispatcher.java:564)
at org.apache.struts2.dispatcher.ng.ExecuteOperations.executeAction(ExecuteOperations.java:81)
at org.apache.struts2.dispatcher.ng.filter.StrutsPrepareAndExecuteFilter.doFilter(StrutsPrepareAndExecuteFilter.java:99)
at com.ibm.ws.webcontainer.filter.FilterInstanceWrapper.doFilter(FilterInstanceWrapper.java:188)
at com.ibm.ws.webcontainer.filter.WebAppFilterChain.doFilter(WebAppFilterChain.java:116)
at com.ibm.ws.webcontainer.filter.WebAppFilterChain._doFilter(WebAppFilterChain.java:77)
at com.ibm.ws.webcontainer.filter.WebAppFilterManager.doFilter(WebAppFilterManager.java:908)
at com.ibm.ws.webcontainer.filter.WebAppFilterManager.invokeFilters(WebAppFilterManager.java:997)
at com.ibm.ws.webcontainer.extension.DefaultExtensionProcessor.invokeFilters(DefaultExtensionProcessor.java:1062)
at com.ibm.ws.webcontainer.extension.DefaultExtensionProcessor.handleRequest(DefaultExtensionProcessor.java:982)
at com.ibm.ws.webcontainer.webapp.WebApp.handleRequest(WebApp.java:3944)
at com.ibm.ws.webcontainer.webapp.WebGroup.handleRequest(WebGroup.java:276)
at com.ibm.ws.webcontainer.WebContainer.handleRequest(WebContainer.java:931)
at com.ibm.ws.webcontainer.WSWebContainer.handleRequest(WSWebContainer.java:1592)
at com.ibm.ws.webcontainer.channel.WCChannelLink.ready(WCChannelLink.java:186)
at com.ibm.ws.http.channel.inbound.impl.HttpInboundLink.handleDiscrimination(HttpInboundLink.java:452)
at com.ibm.ws.http.channel.inbound.impl.HttpInboundLink.handleNewRequest(HttpInboundLink.java:511)
at com.ibm.ws.http.channel.inbound.impl.HttpInboundLink.processRequest(HttpInboundLink.java:305)
at com.ibm.ws.http.channel.inbound.impl.HttpInboundLink.ready(HttpInboundLink.java:276)
at com.ibm.ws.ssl.channel.impl.SSLConnectionLink.determineNextChannel(SSLConnectionLink.java:1049)
at com.ibm.ws.ssl.channel.impl.SSLConnectionLink$MyReadCompletedCallback.complete(SSLConnectionLink.java:643)
at com.ibm.ws.ssl.channel.impl.SSLReadServiceContext$SSLReadCompletedCallback.complete(SSLReadServiceContext.java:1784)
at com.ibm.ws.tcp.channel.impl.WorkQueueManager.requestComplete(WorkQueueManager.java:557)
at com.ibm.ws.tcp.channel.impl.WorkQueueManager.attemptIO(WorkQueueManager.java:607)
at com.ibm.ws.tcp.channel.impl.WorkQueueManager.workerRun(WorkQueueManager.java:984)
at com.ibm.ws.tcp.channel.impl.WorkQueueManager$Worker.run(WorkQueueManager.java:1069)
at com.ibm.ws.util.ThreadPool$Worker.run(ThreadPool.java:1646)

Also,
The following entries are present in META-INF/MANIFEST.MF file:-

Manifest-Version: 1.0
Archiver-Version: Plexus Archiver
Created-By: Apache Maven
Built-By: sunle
Build-Jdk: 1.6.0_29
Class-Path: citiworks-1.0.0.jar struts2-core-2.3.20.jar xwork-core-2.3
.20.jar commons-lang3-3.2.jar asm-5.0.2.jar asm-commons-5.0.2.jar asm
-tree-5.0.2.jar freemarker-2.3.19.jar commons-fileupload-1.3.1.jar ad
gcda-1.34.jar adgcimaging-1.28.jar adgcxml-5.108.jar struts-el-1.2.8.
jar Struts-Layout-1.1.jar jstl-1.0.6.jar cglib-2.1_3.jar cglib-nodep-
2.1_3.jar dom4j-1.6.jar israutil-1.0.1.52.jar soap-2.4.1.jar hibernat
e-3.0.3.jar junit-3.8.1.jar log4j-1.2.16.jar elf-1.3.jar janino-2.3.8
.jar synccache-1.1.jar asm-attrs-1.5.3.jar aspectjrt-1.2.1.jar avalon
-framework-4.1.3.jar axis-1.3.jar axis-jaxrpc-1.3.jar axis-saaj-1.3.j
ar ognl-3.0.6.jar javassist-3.11.0.GA.jar quartz-all-1.6.0.jar xpp3_m
in-1.1.3.4.O.jar datetime-1.0.1.jar cactus-13-1.7.1.jar common-relwas
_V1.6.0-161450.jar commons-dbutils-1.1-20040910.jar commons-httpclien
t-2.0.2.jar commons-io-1.3.2.jar commons-lang-2.0.jar PD-1.0.jar ehca
che-1.1.jar fdsapi-1.0.4.jar drools-base-2.1.jar drools-core-2.1.jar
drools-java-2.1.jar drools-smf-2.1.jar drools-io-2.1.jar dwr-1.1.3.ja
r velocity-1.4.jar velocity-tools-1.2.jar cwtoken-1.01.jar wspmimonit
oring-1.0.jar mqclient-1.0.jar commons-beanutils-1.7.0.jar commons-co
llections-3.1.jar commons-digester-1.6.jar commons-validator-1.1.4.ja
r commons-logging-1.1.jar jakarta-oro-2.0.8.jar jai_codec-1.1.3.jar j
ai_core-1.1.3.jar standard-1.0.6.jar adgcwebutils-1.143.jar xstream-1
.4.9.jar jamon-2.82.jar ce-javaapi-1.0.jar tibjms-4.4.0.jar httptest-
1.0.jar antlr-2.7.8.jar jta-1.3.jar poi-3.0-alpha3-20061212.jar Xenos
-TiffAppender-1.0.jar

That's a class loader issue. You need to check what of hibernate-3.0.3 dependency is causing you trouble. The reason for such errors is that the war/ear contains some jar versions, while the application server global libraries contain other versions, and the class loader already loaded a different version than the one Hibernate expects.

Thanks for the detailed Analysis. Being a newbie wanted to know the places where we need to look into. Also where is the application server global libraries defined. How to look into it.

It is application server specific. You need to check WebSphere documentation related to global libraries and class loaders for that.