The first chef I worked for said this to me when I asked the same question.
"Get a job the biggest hotel you can and learn everything you can....you'll be light years ahead of the interns working here."
He taught classes previously in a culinary school in Colorado and had never been to a class himself. Cooking is a craft AND a trade, with that, experience plays a large roll.
The flip side to that coin is how far do you want to go? My first management job for a corporate restaurant would have been a lot smoother with some formal education to fall back on. Culinary school offers classes that teach you how to manage budgets and subordinates. Controlling food cost, communication, and sanitation. All of these things I had learned from the viewpoint of a line cook. Conveying thoughts and direction to a staff in the manor of a drunk sailor doesn't boad well to restaurant owners and corporate suits. lol
I'm positive there are arguments that pull both side of the rope with strong points. IMO there is no right answer accept the one you make.
I have not gone to culinary school and I can cook circles around every intern I've worked with.
I've worked with culinary grads who have been in the industry for many years and they cook circles around me.
I'm always learning. Reading. Cooking. Eating.
Good luck on the job hunt!
p.s. Hotels are not what they used to be IMO. They have dumbed down food to the point that a monkey can 'cook' it. I've been job hopping the cafes and mom and pop joints to keep my chops fresh and keep in the trends. Maybe you can ask for a working interview and see what's what? I believe that the french word for it is "stodge". I can't spell it but that's how it sounds.