I think this topic may have been done before, and I probably put a rambling post in it as usual. But anyway, here goes.
A lot of folks in here talk about refusing the call and what have you. I like to assume that the Echo would not be granted to a person who would inevitably not have the heroic cajones to do most of what the WoL does. I think Virara has the innate spark that would keep her on the same path, and the same gullibility/obedience. She actually will do a lot of those odd jobs and requests for little thanks as long as she is given food or money for it, or even if they just offered to teach her a thing or two about Eorzean culture. Actually, a lot of things the WoL does, she would do too, I'm not ashamed to admit. She's just not a forward thinker outside of her areas of expertise.
I can think of a few junctures in the story, however, where she might behave differently in a way that impacts the plot.
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Spoiler
1. The raid on the WS: Virara would consider abandoning the Scions here, depending on what stage in her character development this happens. Early Virara and potential late Virara would leave them to their fate and abandon them to the Garleans, working alone from then on out for probably unfortunate consequences.
2. Doman refugees: At least some of them might know her and refuse her help, and she is uncomfortable around them despite sharing their culture. She would not aid them, and thus probably not have Yugiri's critical aid in certain parts of the story, possibly derailing her and the Scions' efforts.
3. The Echo: Virara is already very strong so buffing her with that power could cause serious problems in cases where she mustn't kill someone or avoid overexerting herself. It is likely she wouldn't hesitate to kill Thancred when he was possessed, thus probably earning her the enmity of every ally she'd need to succeed later on.
4. The Company of Heroes Feast: Virara would only need to be told "gather these things and people and we'll make you a feast" and she'd be on it in a flash, no trickery necessary at all.
5. Ishgard: Virara is somehow even worse at diplomacy than a silent protagonist. I have no doubt that Alphinaud would have to work overtime in order to patch up innumerable diplomatic gaffes in her wake, and Ishgard is the place where it would hurt the Scions the most.
5. Leviathan: Virara is phobic of typhoons so this would be a difficult fight to get her into. Maybe she'd have to be blindfolded? But maybe that too could make Levi HM/EX a more interesting fight...
6. Iceheart: Virara doesn't get the Ishgardian grudge against the Dravinians and doesn't care. If the Scions told Virara "Kill Ysayle," she will do so without even so much as listening to her speech. If it's a face to face fight between equals Virara shows respect and a sense of "honor" because that is what she was taught to do. When killing someone outside of those circumstances, what she was taught to do was kill them immediately without fuss by any means necessary. Presumably Iceheart is strong enough to not die to all these cheapshots to the back everyone in here keeps talking about, so her bum rush would probably fail; if it didn't, she'd lose whatever critical clues the foreshadowing Iceheart's dialogue might have had to offer.
More recent events spoilers:
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Spoiler6. The Ul'dah assassination plot: There are several key areas in which it would differ, though the result would be similar. Virara is not some clever artful dodger who'd see this plot a mile away. She is too uncouth to even be around the Sultana, but were it possible that they had an accord before this point, Virara wouldn't see an assassination plot coming if it wasn't aimed at herself, unless it involved methods or ways she understands. She wouldn't have the political acumen to grasp what kind of danger Nanamo is in either. At the rail tracks, Virara would either not notice or not care about the vial. If invited to drink with the Sultana, she might drink the wine first, feeling some pressure from other people who wish to make her better at handling liquor. Virara has some resistance to poison from both training and natural resilience, but it would incapacitate her, and probably allow Lolorito to take a more direct approach anyway. Virara lacks the ability to defend herself in speech to deny murder accusations, and likely would become fugitive without raubahn ever realizing she is innocent, thus taking the brunt of his ire. Her background is sketchy enough that she would look suspicious from the get go, and already her going to eat with a major ruler is hard to imagine. She would probably become a pariah amongst the Grand Companies, with a heavy bounty on her head, and since she likely sabotaged her dealings with Ishgard by being surly, she would have to flee further abroad. As for the Scions sacrificing themselves, they would have to literally sedate or knock out Virara to keep her from recklessly assisting them.
So in general, I think actually Virara, powered by the echo would do a lot of things that the WoL did if she was in those circumstances, maybe even do them well given her prowess at killing things. But in terms of uniting others, showing charisma, being a little bit of a leader or inspiration to others, and in negotiation, Virara falls even shorter, and would probably doom the Scions to failure. If that sounds depressing, it just comes to show that overwhelming strength doesn't necessary mean anything in Eorzea.