What is the United style? I hear this all the time since Fergie retired, but not really at all during his time in charge. The things I associate with his teams are attitude things - desire, commitment, never out of it, a team of winners. They could pull anything out of the fire. I remember that saying, not sure who said it, something like "Manchester United never lose, but occasionally they run out of time".
Under Fergie the most games I saw were against Arsenal, and for the majority of those matches, particularly in the period 2000 - 2010 or so, Fergie was happy to sit deep, defend most of the time, and hit on the counter. He was quite successful with that, but it was hardly any kind of style, it was anti-football, nearly every time we played. So frustrating for me personally, but very effective. Fergie just knew how to win, and that was the way he'd usually beat Arsenal. He'd usually sit Ji Sung Park or someone like that on our playmaker, he'd put a striker or two on the halfway line, and everyone else would be deep, marking zonally most of the time. Arsenal would dominate possession but struggle to create chances, Rooney or whomever would nab a stunning goal or two on the break, and that's how it would be done. Obviously there were games where it wasn't like this, when he sniffed blood for various reasons eg 8-2 when our squad was in disarray, but anti-football was usually his go-to against us.
To me, Fergie was a Manager who adjusted well, he would select specific players and tactics for specific matches. I don't really recall a specific style that he was wedded to. Sometimes you could associate words like "swashbuckling" or "gung-ho" to his teams and it sounds attractive, but again that's just attitude and belief to me, that doesn't explain anything about an actual tactical style, just that the players were committed and had a massive desire to win. To me that was what Fergie was the best at in the world, making his players believe they could win every single game, no matter the situation. And usually that's exactly what they did.