The truly great trainers will use a blend of both methods suited to the dog in front of them. They can use both food and corrections in the training session to meet the needs of their dogs.
You can often tell what a trainer is like from their own personal dogs. Watch how the dog behaves. Does the dog come when the trainer calls them? Can the trainer have their own personal dog off leash? Is the trainers dog good with other dogs?
It is not unusual for a trainer to have younger untrained dogs, but the dogs that they are using for classes should be well behaved dogs.
Look too for a trainer who can train dogs with a variety of methods that suit you. If a trainer can only train with a clicker perhaps they are denying you a method that would better suit your dog. If they can only train with a pinch collar they may be denying you a softer approach that your dog may need.
Plumber and electricians have toolboxes…..make sure that your trainer has a full toolbox to meet all of your needs. That toolbox should include a clicker, a choke collar, a pinch collar and an ecollar…..and a very big sense of fairness for the dog.