Firstly, dam Éowyn. Best Waifu in Middle Earth.
How is she as a card though? Her version is a questing powerhouse, probably the strongest quester in the game. Eowyn likewise has 4 , which is great but is it enough by itself? When you look at the most used heroes with 3-4 , the 3 is just a + while their ability is the main driving force. Arwen Undómiel's insane resource generation, Celeborn being the backbone of any Silvan deck, Elrond having ridiculous versatility, Círdan the Shipwright having reliable and powerful draw, Glorfindel being one of the most OP heroes in the game or as Éowyn being able to increase her to much higher lengths.
Her ability is tough to gage, because it only matters IF you use it. It isn't something you should rely on. There are times where you will never use it. If you don't use her ability then she is just a 4 hero with 6 threat, which is perfectly fine and I can imagine that being a merit for some decks in itself. She also has the powerful Rohan trait, so if you have the cards in your deck she can become a powerful damage dealer, like Herugrim for example, but it's far more powerful on Éowyn and it's in the same sphere too. There is also Golden Shield which is in sphere for , but again.. it's still better for Eowyn. Regardless, ombine these two with Unexpected Courage and you have an absolute powerhouse, or even one of them with Snowmane.
Let's talk about her ability though. It changes the hero to basically a 9 threat hero but it gives her a total of 10 attack for 1 phase, also readying her, so it doesn't matter if you quested with her. Let me just say, this can be absolutely insane. You can destroy almost any enemy in the game. Add a readying affect to her and you can destroy 2 enemies. It's great knowing you have this in case you need it, even if you don't. Not to mention, that 10 attack can help you clear quests with the 'battle' keyword much more faster. These quests can be extremely difficult in the first few turns.
But, she's kind of boring and doesn't do anything special. She's just there, questing and that's it. If you have in your deck then sure, you can turn her into a questing and attacking powerhouse. If you REALLY need to you can kill an enemy or do a battle quest with her ability, but it's really just a panic button, and when you don't use it she's fairly mediocre. You want heroes to define your deck. Éowyn is a hero I feel that you include if for some reason there isn't anything better to add, but you need in your deck along with some form of high and/or you need low threat.