OCB and GCM security
If you look in the OCB submission for CAESAR, you will see that the designers state the security is similar to that of GCM. I would note, however, that GCM has been shown to posses weak key classes, see for example:


https://eprint.iacr.org/2013/144.pdf
https://eprint.iacr.org/2011/202.pdf
http://www.ecrypt.eu.org/hash2011/proceedings/hash2011_03.pdf
https://about.bozhu.me/paper/lgcm.pdf