As the names revealed Comptia Linux+ is well-known for its slate of vendor-neutral foundation-level certs and Redhat Certs are vendor dependent certs. Now also It is powered by LPI (LPI is the acronym for Linux Professional Institute, which also offers Linux certs program) and Comptia recommends Linux+ as a stepping stone to vendor-specific Linux certs such as Oracle Certified Associate / Novell Linux certs.
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Red Hat launched its certs in the year 1999 which is called RHCE. Next in the year 2002 they introduced the entry-level cert is called RHCT. and in the year 2005 and 2006 they also launched RHCA & RHCSS respectively. But the difference is not so much. But as I told earlier, Comptia recommends Linux+ as a stepping stone to vendor-specific Linux certs.
For ur good knowledge, please go thru these links:
For Linux Certs: www.jidaw.com/certarticles/linuxcerts.html and
Linux certs options: www.trainsignal.com/blog/linux-certification-options