This answer has two parts:
- Analysis of the Rey/Kylo Ren fight
- Info from JJ Abrams about the Force
No, we probably can't say that Rey is stronger with the Force than Yoda, Palpatine, Anakin, etc. The following is what we do know.
It is said in the The Force Awakens that Rey is particularly gifted with the Force and it is strongly hinted that she is related to Luke, Leia, and Kylo Ren in some way, or in other words, that she is a grandchild of Anakin Skywalker.
To address the question of her battle with Kylo Ren, we don't have any indication that she was or was not trained in the Force, at least to some degree. She may have been trained somewhat. Furthermore, Kylo Ren was being "torn apart" by the opposing pulls of the light side and the dark side. (See the scene where he talks to the helmet, and the words to Han before killing him, and the track attributed to this scene on the official soundtrack titled "Torn Apart," and various other sources.) In the midst of that personal emotional battle, he killed his father and the result was not what he expected. From the novelization for the movie, emphasis added:
Stunned by his own actions, Kyo Ren fell to his knees. Following
through on the act ought to have made him stronger, a part of him
believed. Instead, he found himself weakened. He did not hear the roar
of the enraged Wookiee above, but he did feel the sting of the shot
from the bowcaster as it slammed into his side, knocking him back on
Amid the rising bedlam and confusion, Kylo Ren struggled to stand. As
he did, so his gaze turned upward.
Add to that the various physical injuries sustained before fighting Rey (Chewie's bowcaster and Finn's lightsaber connections) and then maybe we could be surprised not by her success but by how she wasn't even more dominant.
However, the question might be well-addressed with some interviews with JJ Abrams.
In multiple interviews and Q&A sessions, JJ Abrams said there would not be mention of midi-chlorians in The Force Awakens.1
At one point, JJ Abrams was asked for an in-depth answer and he gave more explanation about his point of view, emphasis added:
"I will just say this: I would never presume to question anything
George Lucas says is canon in Star Wars. And our job was not to negate
or undo. A lot of people who are critics of our Star Trek, and I
respect all of them, said we destroyed what they loved and negated
everything. And we worked hard to clarify that we are not saying that
our Star Trek over-rides a thing of the original Star Trek — it was a
parallel timeline. I never wanted to negate canon that fans held so
dear. And because I love Star Wars and have for too many years… … And
having said all that and meaning it — I don’t want to presume
over-write or change what George says the rules are.
I’m not someone who quite understands the science of the Force. To me
Star Wars was never about science fiction — it was a spiritual story.
And it was more of a fairytale in that regard. For me when I heard
Obi-Wan say that the Force surrounds us and binds us all together,
there was no judgement about who you were. This was something that we
could all access. Being strong with the force didn’t mean something
scientific, it meant something spiritual. It meant someone who could
believe, someone who could reach down to the depths of your feelings
and follow this primal energy that was flowing through all of us. I
mean, thats what was said in that first film!
And there I am sitting in the theater at almost 11 years old and that
was a powerful notion. And I think this is what your point was, we
would like to believe that when shit gets serious, that you could
harness that Force I was told surrounds not just some of us but every
living thing. And so, I really feel like the assumption that any
character needs to have inherited a certain number of midi-chlorians
or needs to be part of a bloodline, it’s not that I don’t believe that
as part of the canon, I’m just saying that at 11 years old, that
wasn’t where my heart was. And so I respect and adhere to the canon
but I also say that the Force has always seemed to me to be more
inclusive and stronger than that."2
1 cinemablend.com source describing some midi-chlorian stuff and citing an MTV interview
2 slashfilm.com source with interview and question posed about if and which character may be non-Skywalker and use the Force extensively in this trilogy