In the Dream World Freddy wins. He turned Jason into a baby, Freddy can teleport and depower The Doctor if he wants. No. I don't see Doctor winning here.
No way does Freddy Stomp. The Doctor is smart enough to figure out it is a dream, and then deduce a way to beat Freddy. He can research Freddy in the TARDIS and find ways of beating him. Besides The Doctor would have the will power to wake himself up!
Freddy loses because he is powerless against anyone who either does not believe he is real or is not afraid of him. I doubt The Doctor would be fearful of Freddy. The Doctor figuring out that he is in 'Dream World' is not out of the question either. Once The Doctor knows its a dream, he should be able to wake himself up. Not the mention The Doctor has previous 'Dream World' experience and managed to escape out of that situation no worse for wear, granted he did have the help of his companions at the time.
The Doctor's perception of the world is so different that I doubt Freddy would even comprehend his mind. The Doctor is not human, he's a time lord, he sees infinite possibilities and time in a whole different light compared to people. I wouldn't be surprised if Freddy got lost within The Doctor's mind. Also I'm 100% sure that the Doctor wouldn't fear Freddy, and that Freddy wouldn't be able to find anything he would fear. The Doctor was able to defeat the Devil, the very epitome of evil. Freddy is outmatched here, even in the dream world.
The Doctor's dealt with a few "Dream World" type characters before, so this isn't anything new for him. Freddy, on the other hand, has never gone up against a Time Lord. The Doctor's mind works nothing like a human's, so Freddy's usual tricks might not work quite like he's used to.