WebSphere Application Server or WebSphere Liberty
Accepted answer
If this is a new deployment we generally recommend WebSphere Liberty. It's lighter weight and the basis for a lot of the new stuff we are working on (for example, RTC clustering new in 6.0.4). The Liberty team has addressed most of the reasons someone would need the full WebSphere App Server, but there are still a few (e.g, applications that very old APIs not in the more modern standards).
One other answer
form more information, refer to : https://jazz.net/wiki/bin/view/Deployment/LibertyVersusWASFullProfileForCLM