Yes. The same features are available to both service account types.
The premium plan offers a range of additional features.
Please note that the benefits will only become apparent once your in-game character is able to hire retainers, so please unlock that feature in FFXIV before considering upgrading to the premium plan.
Canceling the premium plan will revert your account to the free plan.
You will be able to continue using the chat and event list features in the companion app for 30 days after your FINAL FANTASY XIV subscription expires. Due to being unable to log in to the game, features pertaining to items or the market boards will not be available in the app. After 30 days have passed, you will no longer have access to chat or the event list.
The companion app cannot be used with a free trial service account.