Well, let's start with some facts:
- There are direct upgrade paths from 126.96.36.199 to both 12.1.3 and 12.2
- 12.1.3 runs on the Oracle Application Server, including the OC4J web server that EBS users have known for years.
- 12.2 uses WebLogic, standardizing the underlying applications tech stack with most Oracle products as well as Oracle's future direction.
- The killer feature in 12.2 is the opportunity for full availability, made possible through the new hot patching functionality.
- Premier support of 12.1.3 ends in December 2016. Premier support for 12.2 ends in September 2018. (You can fact-check both those dates at http://www.oracle.com/us/support/library/lifetime-support-applications-069216.pdf). That's a 21 month difference, for those who care to plan that far ahead.
So, based on the facts listed above, my recommendation is that either version is a reasonable target for an upgrade from 11.5.10 (keeping in mind that you must be on the reference patch baseline for 11.5.10 prior to starting the upgrade...188.8.131.52). The correct answer will vary on a customer-by-customer basis.
Is 100% availability important to your organization? Do you have a minimal number of middleware-dependent customizations? Are you comfortable with the risk associated with being on a leading (aka "bleeding") product? If you can answer yes to all these questions, I'd recommend looking an upgrade to 12.2.
Does your organization have a large number of middleware-dependent customizations? Are you more conservative in your approach to risk? Can your organization accept system downtimes for maintenance? If you can answer yes to this questions, 12.1.3 is probably the best choice for you...with the understanding that you'll likely be upgrading again in about 3 years.
So, there ya go...my humble opinion on the subject. More questions? Want to talk it over? See things differently? You know what do to - find the comments.