It all started at the 2009 British Open. Nick Matthew and James Willstrop met in the final that ended 12:10 to Matthew in the fifth; the two players exchanged some heavy words, Matthew for example asking Willstrop if he had been taught how to block by Malcolm (James' coach/father).
Before that match Willstrop had his fair share of wins, ever since he hasn't won a single one of their 12 PSA meetings up to date (the last one at the 2012 TOC Final, as video below). There was one occasion when he got close - one that will surely be remembered for long, some calling it even the greatest match ever - a two-hour five-game semi final at the 2010 Canary Wharf Classic. All the others were rather one sided, at least result-wise for sure.
It is rather unusual to have such a head-to-head between two top (very top) players. It must be a mental thing (related to that 2009 BO Final), as we can't say that Matthew would have progressed so much more than Willstrop himself in the last times; in this three-year span Willstrop has beaten several times everybody else (Ramy, Gaultier, Shabana and Darwish) and Matthew has lost a couple of times to players (Peter Barker, Daryl Selby) against whom James keeps winning rather easily and has never lost to (non considering his sole loss to Barker when he was visibly injured, 2011 CW). But it is also a tactical thing.
I just can't understand that after all those losses how come Willstrop keeps playing the same way against Matthew, how come he doesn't try to slow down the pace in a radical manner? He keeps hitting the ball mostly hard from the back, and as soon as they are slightly loose, the 'wolf' volleys them; and as the ball was hit hard, James doesn't accord himself to get back to the 'T' in time. Even Ramy Ashour - the only man who can play at an even higher pace than Matthew - employs regularly slow/high balls to break Matthew's rhythm (and vice versa Matthew doing the same to Ramy).
Another note on the rivalry is that their matches - notwithstanding their personal conflict and the very high standard of squash - do not generate real enthusiasm in the public. As long as commenting/chat was enabled on squashtv, I've seen so many people mocking about "robot 1 having stronger batteries than robot 2..." This is not exactly my point, but fact is that Ramy, Shabana, or Gaultier (even paired with any of the two English men) induct way more emotions and positive reactions from the crowd.
Last note, regarding the relative high number of 'Lets' that occur in their games; Matthew and some others pretend that Willstrop is slow to clear the ball. I think this does not reflect the truth. James has the best hold in the business; if the opponent plays anything loose James will hold his volley and only execute his shot when the other guy has already committed in a way or in another. Hence most players are so clearly wrong-footed, that even if they bump into Willstrop, they are most likely to receive a 'No Let'.
The problem is, that Matthew, on the other hand, can not be wrong-footed easily. Even if he commits as anybody else when James holds his shot, he is so strong and quick to recover and change direction (and subsequently, to bump into Willstrop at times) that he gets his 'Lets' from the referees - am not saying unrightly, am just saying that the interference is not created by Willstrop, but by the player who intercepts the wrong way in these cases.
Anyway, it's a complicated story between these two, and as long as Willstrop doesn't change his tactics radically, it will remain somewhat robotic for us, and somewhat painful for him.