The answer here is actually pretty complicated, and really it is dependent on what your desired result is. If you are truly working to improve your hunting capacity and make your trips more comfortable, you are better off using a weighted pack and following a training protocol that increases TOTAL body strength. The key is maintaining a solid foundation of strength and to establish muscular balance throughout your entire body, with the goal of maintaining joint alignment. When wearing a pack, especially if you have a good one, the majority of the weight is shifted to your hips and down into your legs. Doing so makes you less reliant on your back, abs and inner core muscles to stabilize the weight. Doing so, however, also puts a rotational load on your body as the center of gravity of the pack is slightly toward the back. That's where hiking with a pack is key as it will train your body to adapt. Also, properly packing the bag to pull the center of gravity in as tight as possible is key or you dramatically increase the load as it moves away from your body. Wearing a weighted vest will actually place the center of gravity much more centered, but the load is almost entirely at your shoulders. Putting it at our shoulders also impacts your abs, back and core, however they are impacted much differently. Both training methods will expose muscular weaknesses if they exist that will need correcting. To clarify, as an above poster mentioned a weighted vest caused back pain, more than likely that was just a muscular imbalance being exposed. The issue may not have actually been the lower back. It could be your back, but it could also be your abs, quads, glutes or hamstrings. All of those are connected to your pelvis and any imbalance causes your pelvis to rotate and pull all sorts of stuff out of alignment. If you are limited to only one option, stick with the weighted pack and ONLY do so if you are incorporating it into a well balanced training regime. That being said, the best answer is to use both options for training, and just switch them up. Diversity in your training program will get your body to respond better than anything else.
Lastly, for the love of all things holy DO NOT run with the vest or pack on. If you must to train for an event, do so infrequently and only leading up to the event. The forces that puts on your knees, hips and spinal column are absolutely insane. Let me know if you need any more clarification regarding this stuff.