JFBConnect doesn't automatically add the buttons to the EasySocial registration / login areas. In JomSocial, that's done by JomSocial itself because the have built-in integration with JFBConnect. We'd love it if StackIdeas did the same with EasySocial... feel free to recommend it to them that you'd like that feature in their next release
JLinked for EasySocial does work, but it's a little more limited. The Social Profiles - EasySocial plugin does work with JLinked and you should be able to configure how profile information from LinkedIn is imported into EasySocial. You shouldn't re-install JLinked as the EasySocial plugin is not installed with the latest JLinked version, it's only included in the JFBConnect package.. and JLinked and JFBConnect share the same plugins.
For now, JLinked is still a separate project. With the next major release of JFBConnect (in early 2014), all LinkedIn functionality will be integrated into JFBConnect and JLinked will be discontinued. At that point, all of the features of JFBConnect will work with LinkedIn integration as well.
I hope that helps explain, but if not, let me know!
Thanks,
Alex