Before doing a release upgrade, create a snapshot of your Droplet. Upgrading releases can lead to some rather unexpected results if your application isn't compatible with new software versions that will be installed when you upgrade.
For example, I'll use PHP. Older Ubuntu versions have PHP 5.x in their repositories while the newer releases have PHP 7.0.x. When performing a release upgrade, PHP 5.x becomes 7.0.x, so any PHP applications on the server that are not fully compatible with PHP 7.0 break instantly.
The same is true for many languages.
My recommendation would be to deploy a new Droplet with Ubuntu 16.04 and migrate your app over to it instead of upgrading the release, unless you're sure newer software versions will not break or cause issues with your current application(s).