Contrary to the popular opinion my rating as an Indian fan is ;
Cook 1 actually for me. Best opener. Technically sound. Most complete opener. Had no issues vs spin swing or even pace. Bounce maybe to an extent but overall best with no weaknesses really
Number 2 for me is actually Hayden. Less weaknesses than shewag. Shewag was just absolutely pathetic vs swing in England and SA too.
Number 3 I was about to say smith but I think shewag takes this one.
Smith was a little bit suspect vs good spin and bounce.
Yeah, Cook's a bit underrated when compared to other openers (and a bit overrated when compared to other english openers)
All 4 had flaws.
Matthew Hayden — was basically weak against any form of sideways movement, had a flawed technique against sideways movement but had the mental strength to counteract it and make some nice tons in England and South Africa, honestly an Okay player of sideways movement, but his great strength was his ability to easily counteract and overwhelm high bounce and spin, and absolutely slaughter teams on any flat wickets like there is no tommorrow.
Alastair Cook — in the late stages of his career, he wasn't that capable against true pace anymore, declining hand-eye coordination probably, even at peak he had struggles if the opponent was a tall fast bowler who could get inconsistent bounce at high speeds and also seam the ball sith a good zip, like Ishant Sharma and Morne Morkel. One of the best ever white plays of spin, amazing against high pace/bounce, also struggled a bit with sideways movement (seam) but mentally strong enough to hold his ground and beat the shine off of the ball, less of a FTB than Hayden but much more skilled against swing/seam and even tougher. if the conditions suited him and the rest of the team was anywhere near competent (remember, English batting was substantially weaker than South African, Indian and Australian during the careers of these four), he was almost impossible to get out.
Virender Sehwag — had no technique against sideways movement at all, would immediately mentally concede against it even at home, was genuinely a tail ender in England who somehow got to open, if he played in any era other than the super flat 2000s then I don't think he'd have much of a career but he was lucky, however he was an absolute ruthless beast on a flat wicket, and perhaps the greatest batter ever against any form of spin bowling, turned Shane Warne and Muttiah Muralitharan into gully bowlers many times.
Graeme Smith — an amazing player of swing, his stats in England are a bit exaggerated due to double hundreds on two roads but he was always amazing against swing, but seemed to struggle predicted bounce in South Africa and could never handle high bounce in Australia but played a couple good knocks, not a very good player of spin at all. Very talented at counter attacking side ways movement but not really good enough at home or India and Australia, making runs in England is fine but Newzealand of that era had a nothing bowling bar Shane Bond who was injured half the year, more capable against pace and bounce than Sehwag was against sideways movement though.
at the end of the day, it is a coin toss between Chef and Big Haydos, and Hayden has certainly the argument to be better but opening against dukes in England is probably the hardest thing to do tbh, and Chef did very well in Australia while Hayden always failed to England.
so basically, the two big tours that Chef has, the Australian Ashes and the Indian triumph, combined with the longetivity and having such a harder job than Hayden and Sehwag who faced Kookaburras on Indian/Australian 2000s wickets while having amazing batting lineups to lean on, I'd give it to Chef.