You can probably get the exact same training effect by slamming a medicine ball into the ground anyway.
How diverse can one workout be? Try time under tension, perhaps? Pyramid-style with heavier/lighter weights? Flipping the tire after so many hits? Superset it with seated dumbell presses (there's a Derek Poundstone vid on the bet of him doing this - gruelling stuff!)?
What do you mean 'swear by it'? There's no super special training exercise that is above anything else. It's just a general power training exercise, there would be no different training effect than slamming a medicine ball against the ground. You're swinging something towards the ground with a whipping motion, developing RFD and core stability. Neither exercise is going to specifically develop punching power, only punching does that. The different load and the swing towards the ground ensures that the kinetics and kinematics are completely different than punching. I wouldn't waste my money on that equipment unless I'm trying to kit out a gym with different tools for some group circuit training.
Anything and everything. More important is what specific physical ability do you want to develop, and how you're going to progress it. That's also dependant on your training status and where you are relative to your competition demands. Everything has a place at some point in the training year, even exercises that I don't really like for boxers like deadlifts and kettlebell swings have their place in the general prep phase. If you do the basics well - squat, hip hinge, jump, clean, bench press, bench pull/pull ups, throw, train good scapula mechanics, learn to separate your hips from your shoulders then you're ahead of 99% of people anyway. You don't need any key lift, no specific exercise is going to make THAT much difference unless it's training something you've completely neglected. An athlete (that's what a boxer/fighter is as well, nothing special about them, still human) should have a well balanced, well rounded physical preparation.
I was thinking - as indicated by my OP - more suggestions as to brands people trust for each piece of equipment, not so much routines. I've done tire flipping, though, (mixed with anaerobic sprints and jumping in & out the hole) and found it to be a pretty effective full-body workout. :good