I think I'm going to bow out of the debate, since it's getting pretty late and this is one of those fanboy debates that could go on until a participant collapses on their computer out of weariness and dehydration.
Instead, given that there are 2 main points of contention about Ray's capabilities, I will address them as best I can.
The Mind Battle
Okay, here's what we know about the force with regards to the mind: It works through it, so if someone is weak willed, they will succumb to the powers of mind suggestion. If they are strong willed, they don't. That is all the explanation we are given in the originals and as far as I can remember, since then. What Ren seemed to be doing was an elaborate version of that, battering down minds until he gets the suggested. Theoretically, his could take him a great deal of time, and is dependent on weakening his victims. For all we know, taking the information from Poe could have taken numerous attempts that we just didn't see because that'd have fucked up the pacing.
However, Ren has also been greatly strained by the movie at this point, with many doubts resting on his unstable mind. With Ray, she had just gotten in, and just woke up. She's perfectly okay, and naturally strong willed and strong in the force. Given enough time and attempts, she probably would have succumbed, but it's not so unbelievable that she would be able one of the few able to hold off one force mind attack, compared to Poe, who is also probably strong willed, but also has just seen his village exterminated, lives ruined, and knowing he's probably going to die. Poe's badass, but he's had his life flipped over in a desperate struggle for a last ditch effort that he lost in battle. Compared to him, Rey is stronger, better rested, and in better morale, while also being strong with the force, against a more unstable Ren. She wouldn't have held out forever, but it's not impossible that she could fend off one attack, but Rey managed to escape before attempt 2 could be started.
The Final Battle
A lot of people have been focused on speculating about Kylo Ren's abilities and training and fighting condition. But I think we've been forgetting one very important thing: Emotional stability is the largest key to victory in a force battle (assuming high ground isn't available). Obiwan only lost the fight with Vader not because Vader outclassed him, but because he deliberately allowed himself to take a hit so he could become a ghost that haunts Luke. He was the more emotionally stable of the two, and he was perfectly matched with Vader. And it should be noted that Luke was at the height of his power when he talked to Vader in RotJ, while Vader was at his weakest when he was torn between wanting to play the dark side part and loving his son. The emotional stability burned him up, and Luke finally bested him when he was fully focused on protecting someone he loved: his sister. Momentarily, there was no conflict there. It's only when he realized that he was his father did he put down his lightsaber, and then he was downed by the emperor's lighting. Because it was a sneak attack, perhaps, but it was also by coincidence a emotional struggle for him to decide whether to be angry and protect his sister, or be merciful and save his father.
So lets ask: How is Kylo Ren feeling at the time of the battle? Dude just stabbed Han Solo, his own dad, with his flaring lightsaber and looked into his eyes as he died and fell away. He couldn't even do it himself, he had to have his father 'help' him. If he was unstable before, what about now? I doubt that his struggle is over by any measure. If anything, he's even more anguished by the thought. The problem is that the dude has sentimentality and he knows it and he thought killing his father would kill it, but it didn't. Half the time of through the fight he looks like he's holding back the biggest pain in his face, beating his wound almost like he's punishing himself, perhaps believing that pain gives him strength.
Meanwhile, people call bullshit about Rey being reminded of the force being the key to her winning, but.....well, isn't that how it's always worked with Luke? Rey is introduced as a character looking for identity. She wants to believe that her family will come back for her, but being so dependent on a connection that will never return left her as this random scavenger in this random desert world, with no body there to be with. Her only relationship there was her bringing parts to that one scumbag. Her only identity is as a lost scavenger. Her character development has been about finding her roots as a pilot and now as a force user. That was what the entire episode with the orange lady yoda was about. And then, she constantly used the force to escape the First Order's base. So when she remembers that she is a force user, she is finally taking the mantle of her new identity as a Jedi to heart, and that is empowering....emotionally, and therefore, as far as the force is concerned, physically.
Ren is better trained and a better fighter, but he is at the absolute weakest of his abilities right now due the freshness of his patricide, while Rey has just been symbolically born anew. That's what tipped the odds in her favor.
