Han Solo is, yes, it's true, unique, and he gets all the leaway that his reputation implies here. Solo isn't just a faily "good" pilot, but one of the luckiest bastards alive in the Star Wars Galaxy, and that counts for something; Solo is unpredictable, and his very character is above silly, fanboy debates like this.
Without jedi pilots Captain Han Solo,is in my opinion, undoubted top of the star wars pilots. However, considering the skills of the force sensitive pilots I would have to put him at a close SECOND to Anakin. But give Han his beloved Falcon I would say his innate knowledge of the falcon, luck, and superior piloting skill, I honestly believe he would be able to best Anakin in a dog fight. Not necessarily killing Anakin but forcing a retreat from him. The Falcon is a vastly superior craft to any starfighter flown by anakin throughout the Star Wars timeline, and with Solo at the controls he would outfly any pilot/ship combo.
The only time Han ever bested Anakin/Vader in a dogfight was in ANH when he caught Vader and his minion TIE Fighters by surprise due to Vader focusing on Luke. Without the element of surprise on his side, Han would get brutally raped by Anakin (without lube) in a dogfight. Plus, Anakin could use the Force to grab or crush Han's starfighter in a second.
First of all there was only ever one time where they flew ship to ship and that was the death star trench run. Han already bested him. 1-0 Han.
I would say Han would best him in a straight out dogfight if he was in the Falcon, and Vader in his TIE. The Falcon is a better ship, and a pilot is only as good as the vehicle he is in.
Additionally I think that the jedis are not as powerful as fans believe them to be. After all the force unleashed is (as stated by Lucasarts) "an overexaggeration of the force" so....NO JEDI COULD CRUSH AN OPPOSING SHIP WHILST IN A DOGFIGHT!!! remember EU has shown many instances of non-force sensitives defeating jedi or sith in melee/vehicle combat. E.g. sw old republic.
Han himself killed the clone of Palpatine by shooting him in the back, and additionally he fought and killed some dark side adepts in the latest fate of the jedi novel !!
Now all you vader fans cannot say that han surprised Vader at the death star because that really contradicts the fact as an uber- uber powerful jedi his powers of precognition should be half decent. Remember we are dealing with Vader! possiibly one of the most powerful jedis ever.
Vader was distracted with Luke, because he felt that Luke was strong in the Force. Also given the fact that Vader thought that he had destroyed all the other X-Wings in the trench with Luke, I'd say that, yes, it is fair to say that Vader was caught off-guard when Han came in from above, as he was more worried about the possible threat of a Force-using opponent than he was about any other threat.
Qui Gon says a jedi sees things before they happen. Therefore a sith as powerful as vader should of seen his wingman crashing into him, or the falcon shooting his sorry ass. He has no excuse for being distracted with Luke either.
It just proves that force users are vulnerable, it proves that the Jedi are overhyped not Han.
Han in the Falcon would take vader in his TIE X1. Auto tracking quad lasers, superior sublight speeds, concussion missiles, and shields that can take hits off an IMP star destroyer would trump Vader in his X1. Vader would be punching his hyperdrive button before Han blows him to pieces.
Ummm, The Falcon shot the Wingman in the back, which then spun into Vader before he could react. The space between the wingman and Vader was too small for Vader to react in time. In this situation, it is in an open area of space. Vader's Tie Advanced X1 has a shield generator and has much better weapons than standard TIE fighters. He also has the force to improve his aim. Vader is easily fast enough in his X1 to evade the lasers of the Falcon.
Never once have i said Han is all powerful... buddy.
Vader vs Han on foot, or the same vehicle, Vader takes it every time. Vader in the X1 vs Han in the Falcon, only then would Han come out on top.
As Darth_sadow1 says Vader may be fast enough to evade the autotracking quad lasers in his X1, but he would be doing so many evasive moves that he would be lucky to get even one return shot at the Falcon. And if he did it wouldn't matter, because the Falcons shields eat star destroyer laser for breakfast.
Now If Vader shot one of his concussion missiles at Han, the Falcons auto-tracking would shoot it down, thats before han would even have to waste his electro countermeasures on it.
The X1 shields are decent, but even a few glancing shots from the Falcons vastly superior quad lasers would be enough to worry Vader. Han also has his concussion missiles he could use on Vader, and forward firing retractable blaster, not too mention his Solo luck, and incredible piloting skills.
There is just no way Vader could overpower Han in this specific circumstance. The force cannot make a ship faster than its engines allow it to go, or give it better shielding, therefore Han forces vader to hypersapce jump, or otherwise the dark lord of the sith becomes one with the force at the hands of a "stuck up, scruffy looking nerf herder".
P.s. Sadow, because vader didnt react in time, or dindn't forsee his wingman getting shot up, this shows that sometimes luck prevails over the force. AND maybe the jedi are not SUPERMEN, and they are vulnerable (as Lucas has previously stated).