I know that I'm going to be massacred for this, but he is getting a bit overrated here. You don't often see players who can impose themselves on the game and be a consistent match-winners from fullback positions — like Roberto Carlos, Cafu, Lahm or Dani Alves did at their best. Irwin was ridiculously complete — two-footed, can play on either side, very balanced in terms of his defensive and offensive contribution, but he had rarely won games on his own. Roberto Carlos was worse defensively that Irwin, but overall he was a more influential player — which is why he had almost won 2002 Ballon d'Or (finishing as a runner-up to Ronaldo in a very close race), got 2nd in FIFA World Player of the Year vote in 1997 and thrice became the best player in Brazilian league. Generally he was considered as one of the best players in the world at his peak. Denis Irwin was considered as one of the best fullbacks in the world in pretty much the same timespan, and there's a difference. You shouldn't trust those awards blindly, of course, and Carlos' marketable personality played a role in that, but it's hard to find objective arguments in those subjective comparisons.
Denis Irwin was fantastic — probably our best fullback ever (only Evra can compete with him, but I see why you'd choose Irwin over him) & generally a stupendously consistent player who won't look out of place in any team. But when you compare him to the very best, it's a bit like comparing Rooney to Messi (taking a play straight from your book), obviously taking different requirements for forwards/fullbacks in consideration — comparing a genuinely world-class generational great to one of the all-time greats.
Andreas Brehme is probably a better comparison to him, as he's much more similar to Irwin — both were two-footed, could play on either wing as either a full- or a wing-back, were taking penalties and free-kicks and also had an outstanding defensive presence, but, again, Brehme had scored a winner in the World Cup final and won Serie A Player of the Year in Inter Milan's title-winning season (competing against the likes of Maradona, van Basten, Gullit, Rijkaard, Matthäus, Baggio etc.).