My understanding is that your metabolism returns to baseline relatively soon after you complete light or medium intensity steady state cardio. It is only after intense resistance or burst (HIIT) training that your metabolism remains elevated for some time. More bang for the buck. You get out what you put in. No free lunch, and all that. https://www.cbass.com/hiit_rejuvenate_aging_muscles.htm https://www.cbass.com/intervalshealth.html Also, to keep your basal metabolic rate from declining, you need to hang onto (or increase) your muscle mass: https://www.cbass.com/METABOLI.HTM
This guy had an insane metabolism and trained like an athlete with weights to develop strength (one student said he could press a 75lb. barbell straight out in front of him from his chest and hold it there while standing), cardio (ran 3-4 times a week for a few miles and would change his pace repeatedly for high intensity workout) and diet. At 140lbs., abut 5'7" and never used PEDs.
The answer really is neither will substantially increase your rate of energy expenditure throughout the day. Even a HIIT session the EPOC response maybe utilizes an extra 100ish or so calories. We’re also talking an actual HIIT sessions not what people think is HIIT. The “after burn” as it’s marketed isn’t all that it’s cracked up to be.
Apart from the calories burned, my understanding is that if the exercise is intense enough (anaerobic?) you deplete your glycogen stores and maintain/improve insulin sensitivity. This reduces the risk of developing metabolic syndrome and helps metabolize fat. The other thing about meaningful (resistance) exercise is that it helps to maintain or improve lean body mass. The more lean body mass you have, the higher your metabolism is, even at rest. So while I agree that you do not burn much in the way of calories in any one workout, however intense it may be, including the "after burn, there are more variables at play.
I think if my memory serves me correctly the body stores (depending on how much muscle you have) roughly 2000 calories worth of glycogen in skeletal muscle. The whole “depleting glycogen” thing is also overstated. If you went on a long fast maybe then you’d be depleted or ran some ultra marathon. I suppose the question I’m asking is how are we defining “metabolic burn”? Metabolic rate is utilizing calories for energy in which case no exercise is going to significantly increase your metabolic rate hours and hours after exercise except sorta like you said, building more muscle through resistance training moreso if you’re a complete noob. Your RMR isn’t going to increase all that much from resistance training unless you’re that noob and put on 20lbs of muscle in a year. After that, putting on a couple of LBs of muscle here and there how much more “metabolic burn” am I getting through resistance training?
You're right. There is the question of materiality. But as they say, "The journey of a thousand miles begins with one step." And you want to make sure that those steps are taken in the right direction. If we are talking about burning calories to shed fat, the first prong in the process is the dietary regimen. Meaningful exercise, the second prong, becomes necessary to maintain lean tissue while in caloric deficit. Because if muscle is lost while in caloric deficit, then the body is working at cross purposes with the fat loss objective due to a corresponding slowdown in metabolism resulting from both the reduced caloric intake and the loss of lean tissue. (We both know this to be true.) I can't speak to the numbers, only the general direction and of a cumulative effect over time.