No, definitely not but I do think that she has been (and still is) a Successful Actress.

For my own tastes, I'd have to give it to Emily because when I know she's in a film, I want to see it. I can't say the same for Anne Hathaway.
This. I watched Sicario and want to see Girl On The Train for this exact reason. Anne Hathaway doesn't make me want to watch a movie.
I have a brain and good taste, so no, I'm not part of the target demographic.

Probably more successful since Anne narrated a political documentary.

Agreed.

Define successful.
To me, successful isn't defined by how much money she's made. That's something US citizens care a lot about but it means frak-all to me.
I think she is a success if she is happy with the way her career has gone.
So, you'd have to get Anne and her together and see who seems to be happier with their careers.
Anne did that Batman film- so I had to give her a lot of negative points for that, just as I had to do for Marion Cotillard (although Marion more than made up for it with her portrayal of Edith Piaff).
Anne gets points for her recent sci-fi film, Interstellar, which I quite liked but honestly, I can't think of that many Anne Hathaway films that made a big impact on me. Brokeback Mountain was really good but not because of her.
For my own tastes, I'd have to give it to Emily because when I know she's in a film, I want to see it. I can't say the same for Anne Hathaway.

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Depends on how well she acts. Not everyone needs their name listed on a movie. The important thing is that she has enough to live happily. Not ever after because Drew Barrymore didn't say so while riding in cars with boys. What?
When you expect the world to end at any moment, you know there is no need to hurry."

ScarJo getting proper lead roles? Like in The Avengers? Or the voice in that goofy Joaquin Phoenix movie? I don't think SJ is capable of handling a serious dramatic lead role. Emily Blunt has proven it time after time.
I'm not a woman much less Deanna Durbin, but the old-time glam-shot appeals to me.

She seems to finally be getting films where she plays the lead role rather than supporting a leading man so her career is definitely on an upward trajectory. Not unlike Scarlett Johannson who had a similar ten year wait before she started getting proper lead roles.

Blunt is very successful and nobody can look down on her career but no her career hasn't been as successful as Hathaway's yet. I know the Oscars get made fun of but they do matter and Hathaway has one while Blunt does not and Hathaway has more hit films under her belt as well. Hathaway like all actors has had flops but Blunt has had more big flops and under-performers.
I think the Mary Poppins role is a good one for her and so is her role on The Girl on the Train. Now lets just wait and see if one or both of those films are successful.

Absolutely agree.
Ignorance isn't bliss. Ignorance is laziness. So stop being so lazy!

No, unfortunately. However, she has always been highly regarded as a talent. She started her career as a chab68racter actress and is just getting better and better. Hathaway started as a Julia Roberts look alike, became bankable and can act for sure. Still, I see Anne's star dimming and Blunt just getting more compelling each year. Emily can act circles around Anne who is frankly overrated for the talent that she possesses.

"It depends on your definition of "success"."
More importantlywho cares?
Sometimes ya gotta wonder.

It depends on your definition of "success".
Compare their filmographies at Rotten Tomatoes and Metacritic.
https://www.rottentomatoes.com/celebrity/162685827/?search=emily blunt
http://www.metacritic.com/person/emily-blunt
https://www.rottentomatoes.com/celebrity/162656190/?search=anne hathaway
http://www.metacritic.com/person/anne-hathaway
But Anne won an Oscar and is more famous.

Nope. Not at all. Hathaway has been in 2 films that have made a billion, 2 Oscar nom, including a win, 2 films that were nominated for Best Picture, and an Emmy. Blunt has some notable flops to her name, more than Hathaway has, a missed opportunity to become the highest grossing actress of all time, and her only big award is a Golden Globe. And not to be rude, but how does a 54-years-too-late sequel to a beloved film sound like it's "looking good"?