I've been playing Grand Kingdom for a couple of months now and I can say it runs really well on the Vita. To my knowledge it's virtually identical to the PS4 version.
The game has plenty of story missions but it's really all about the gameplay, which hasn't gotten old for me. You have a lot of options in terms of developing a unit and strategy.
There's a very good tutorial which will help you along even if you've never played a turn-based tactical RPG.
The online component is well made; it's asynchronous which means you're not directly fighting other people, but the squads they've put together, so there're no waiting or really any of the annoyances that come with online play.
You can also choose between English and Japanese voice acting; both are good in my opinion.