You can tell a lot about a person by doing some reading. Both Chef Ramsay and Chef Irvine have published books about themselves and their cooking.
The OP mentioned Chef Irvine in Kitchen Nightmares. Chef Irvine is not in any episode of that show. In that episode, Chef Ramsay was at an Italian restaurant in Long Island, NY named "Peter's". The big, beefy guy who was yelling and cursing was the manager and brother of the owner of "Peter's". His name is Peter Pelligrino, and I suppose he might look a bit like Chef Irvine on quick glance.
I am a fan of each of the chefs. Each has a cooking and leadership style that are at the same time delightful and insightful.
Chef Irvine is a master event planner and cook. Anyone who can cook gourmet foods at the incredible level of precision that Irvine does, all while cooking in conditions that are truly less than ideal, is a master. His "kitchen" conditions, per the show's theme, is what makes Chef Irvine shine. He has had a tremendous success in his career cooking for the royal family, US presidents, special events, etc. D:I is an excellent display of his prowess to "make it work". He and Chef Ramsay are totally different. I don't believe Chef Ramsay cooks for massive crowds, served all at once, buffet style using huge commercial pots and pans. Chef Irvine's cooking is "large scale" while Chef Ramsay is individual servings made to order.
Chef Ramsay has numerous Michelin stars spread across his restaurants. I believe his only failure was the Glasgow, Scotland restaurant that didn't meet the tastes of the clientèle location. His staff are loyal - his restaurants are run by chefs who have worked for Chef Ramsay for years. His trust is in them for one reason alone - they consistently meet his high standards. Call him a callous prig if you must, but don't believe for a second that he does not know his food, restaurants, and staff. Yes, he yells a lot on HK but those cooks don't meet his standards and that is the demand of them in that show. (Plus the drama!)
I'd work for either chef at any moment's notice and learn absolutely everything I could.
(Side note: HK is a British show. Chef Ramsay was the man at the pass during season one. I believe Chef Marco Pierre White is at the helm now. The US version is a cousin to the UK version. As is Kitchen Nightmares.)
"Honey, is something burning?" - my wife