In a business setting it wouldn't be appropriate to migrate to a new version of anything simply because it exists. The expected benefits need to be weighed against the drawbacks. Even if no code changes are required (which is entirely possible when upgrading to a newer Java version), there's an overhead in sys admin time, possible system downtime, testing effort etc. Developers wanting to use the new features aren't the only stakeholders involved.
Learning the new features of Java can be challenging, but most of the difficulties are probably organizational. I agree with Ulf that you need to weigh the cost versus the benefits. When migrating from Java 7, I suspect one problem you may encounter is the temptation to rewrite existing code to take advantage of the new features. Using the latest and greatest approach can be appealing but ultimately it is a business decision.
One area that might cause problems is tooling. For example, we rely heavily on New Relic for monitoring and they do not have production-level support for Java 8 yet. Their 3.8.0 and 3.9.0 libraries have only "experimental" support for Java 8 and only for Java 7 compatible code running on the Java 8 JVM and they are saying not to use Java 8 in production with New Relic yet.