The “Here’s What I’m Thinking” fight scene: This form of fight scene is a stop-and-go approach, pausing the action to examine what the character is thinking or feeling. Balance is extremely important in this method. Too much focus on the internal thoughts and feelings slows the action and kills all the excitement. Most authors tend to use this in some form or another, but the martial art fight scene writers tend to use it the least, opting instead for describing the mechanics of the fight.
Example: Fall of Angels (1996) by LE Modesitt, Jr.
At the scream, Nylan blinked, then lifted his blade as a bearded armsman bore down. The engineer wanted to turn and flee, but he'd just get himself cut down from behind.
Nylan barely managed to get the blade up to deflect the smashing blow, and his entire arm ached. He urged the mare sideways, raising his own weapon again, and hacking the bearded man, who caught Nylan's blade with the big crowbar. Again, Nylan's arm shivered, but he actually gouged a chunk of iron from the huge sword.
He wished he had had the time to try his shield idea, but the armsman brought the huge blade around in a sweeping, screaming arc, and the engineer was forced back in the saddle. He could no longer see what else was happening, though he could feel the lines of white-red force flying toward and around Ryba.
Almost automatically, as the attacking armsman overbalanced, Nylan felt the moves that Saryn and Ryba had drilled into him taking over, and his blade flashed-once ... twice.
What makes it work:
The writer takes the time to tell the reader what the protagonist is feeling and thinking, and what the protagonist extrapolates from events as they happen, giving insight to the character and making the protagonist more sympathetic to the reader.
Notice above that Modesitt uses a balanced mixture of long and short sentences, and that the sentences are also balanced between the protagonist's thoughts and action of the fight. If this is the style you're going for, this balance is crucial.
Why it doesn’t always work:
A lack of details in the fight can sometimes create confusion that pulls the reader out of the story in order to puzzle-out exactly what is happening. When the scenes have too much internal focus, the reader loses the pacing of the fight--in other words, the fight gets boring.
Modesitt uses several “as X did this, Y did this” constructions per fight scene--many include actions that are not really happening at the same time and could have been written in the order they naturally occurred; however, Modesitt never uses them so much that they become distracting. When in doubt, get rid of the "as X." We authors think that "as X" constructions speed the writing up, when in fact they actually slow it down.
Notice that no technical descriptions where given to any of the movements that would imply formal training, but there are references to acting without thought due to hours of practicing. If your more inclined to get into the mechanics of the fight, read entry #1 on "The Martial Arts" fight scene.