I haven't played Hyrule Warriors, so I can't comment on the mission structure. But in Dragon Quest Heroes you have a small hub world where you can buy Weapons, Armor ("Orbs" in this game), take on side-quests, receive mail from various NPCs you help out or story important characters, an Alchemist you can create accessories with various stat boosts, the Medal King who you trade in Medals you collect through various means in the game for rare materials for alchemy or straight up powerful weapons and armor, and lastly you have a bar where you can switch out your active party. You have up to 4 characters you can switch control of on the fly in battle. There's also a World Map where you choose your destination whether it be the main Story missions, side-quests, or revisiting old areas where you can fight enemies endlessly for Gold, Ingredients, and EXP. As a pure Dynasty Warriors/Musou game I'm sure you can find some fun with this game, but I think you'll get the most enjoyment out of it if you're a Dragon Quest fan as well.
If you'd like to see the game firsthand here's a shameless plug to my stream where I'm currently playing it
www.twitch.tv/boogiepop
Despite being a big Dragon Quest fan, nothing from the CE really struck me as amazing, so I just got the regular copy of the game.