Erelith loves the rush and thrill of life. Where Mira's more reserved, Erelith is more openly passionate. She cannot fit comfortably into a mold, and certainly has a harder time being able to separate herself from the Inquisitor role than Mira does. While it's not easy for Mira either (at all, given her humility and caution towards her own shortcomings), she at least clearly sees the reason to serve as a symbol towards the people doing so gives hope to.

Mira never claims to be holy. She simply hopes what she's doing as Inquisitor will be enough. She longs for a sense of safety, security, steadiness, and being seen as the human being she is. She's exhausted by the end of it all and is quite happy to retire to a quieter life with her husband. To Mira, there's freedom enough in pursuing one's passions at one's own pace, building a home full of love and friends, and doing good as she will. There's freedom in simply being Mira---not Lady Trevelyan, not a mage, and not the Inquisitor---and doing what she wants.

What she wants is to experience life.

Erelith cannot separate the pressure of being Inquisitor from herself. She's always searching for some piece of her that's missing and is always evading her. Too much structure and the thought of being caught in too "small" a world drives her mad: she constantly needs to be moving and on the go. She constantly seeks more but has trouble defining what that "more" is. That often drives her to be impulsive. It drives her to more quickly and decisively analyze risks, and she's far more likely than Mira to take them.

She struggled with her clan's small, isolated world. She struggles with the bounds being Inquisitor brings and having to walk on eggshells around nobles (which Mira hates too, but is more accustomed to by having been born into that world and dealing with Circle politics).

Meeting Solas is like finding someone on the same wavelength for the first time. The way he thinks and his journeys into the Fade paint a picture of a life that goes well beyond what she's ever imagined a person could achieve. He sees and understands worlds and creatures beyond the bounds and constraints of humans and the Dalish alike, and while they butt heads a little at first, she finds the way he thinks and speaks intoxicating. She wants to experience what he has (at least, what she interprets these experiences to be).

She feels a rush around him. Solas is exciting to her. Erelith's own sights are ever-expanding, and being near him and talking with him just syncs with that part of her brain that craves more. She kind of likes someone going toe-to-toe with her too even if she doesn't realize it's freaking Fen'Harel.

Mira wants to be part of this world (where she never felt like she was or could be before).

Erelith has always been too "big" for it. I think she's never understood just how deeply that runs or why that even is, and I suspect it's going to play a big role in her story.

I also think it's quite funny to consider how differently they think about the other's love interest, too.

Mira loves Solas. She is genuinely intrigued by him and could spend hours discussing magic, philosophy, and listening in mutually fascinated, shared respect towards each other. Yet they're so very different in terms of their lives and what they want from them, and they're not attracted to each other. Mira surprises Solas and undoes a lot of what he's believed about humans, and he cares for her as a friend.

Erelith gets along fine with Cullen even if she doesn't really "get" him. She respects him and what he's doing for the Inquisition. She has eyes, so I think she would make the simple observation that he's good-looking, but it wouldn't go beyond that.

Yet I also think if she were stuck in a room with him long enough, she'd throw herself off a cliff.