I only feed live rodents to hatchlings until they accept pre-killed or frozen/thawed. Personally, I prefer feeding freshly killed mice to my animals simply to avoid any instances of rodent-related injuries. Many years ago when I only owned a few snakes we did feed live but after one of our snakes received a nasty bite from a rat we put an end to that. That snake still has remnants of that scar and it serves as a reminder for me of why I kill the rodents beforehand.
I don't think the snake finds any more enjoyment out of eating pre-killed mice than live. The snake simply wants to eat. It's not a game or sport for them, it's just in their nature to find prey and consume it. Their enjoyment comes from having a fully belly.
I'm not sure about frozen rodents losing nutritional value. Unless they've been frozen and shelved for a long period of time, I would think the nutritional value would be no less than a freshly killed rodent and most frozen rodent suppliers don't freeze their mice/rats until the order has been placed. Please correct me if I'm wrong. I don't ordinarily use frozen feeders because I buy live from a vendor along his route.