Is Java for OSX 2013-005 from apple a JDK6, or just a JRE?
It is the JDK as noted in the path /System/Library/Java/JavaVirtualMachines/1.6.0.jdk it installs into , and also seeing what files are installed there.

As far as I understand the removal does not change Java but removes plugins from browsers

However I would use the later JDK for Java 7 from Oracle as there are some improvements in the environment and language as per Oracle's release notes