First of all, note that I absolutely agree that exercise will matter a lot. I don't agree that it will make a huge difference in BMR
for someone who maintains similar weight though. What it will certainly do is simply burn lots of calories both through the exercise itself, and short term increase in metabolism, as well as increase your energy levels to a point where you may end up being more active outside of exercise too.
But about BMR: Lean body mass between two people of same height and weight can certainly make a difference, but people tends to overestimate how much of a difference it will make assuming weight stays relatively similar.
(Note that difference in lean body mass certainly can have very substantial effect when you ignore large differences in weight because that opens the door for much larger variations in lean body mass, but note that bronbron was explicitly talking about similar weight)
I'm an amateur power lifter. My lean body mass after abut 10 years of exercise is about 15kg higher than when I was pretty much the same weight but fat. If I'd stated lifting younger (I was about 30) or used steroids, or spent more time with a trainer early on learning the right way to train, I might have added substantially more, but people tend to overestimate how much muscle you can realistically add. My current weight and performance means I'm an advanced lifter, within the top 10% of gym goers easily.
I often see people think they need to add on huge amount of calories when they start exercising, but that's rarely true. My average calorie intake to maintain my weight including what I burn during 3+ intense weight sessions a week, at a weight of 106kg is about 2400. That is not estimated, but measured by tracking weight + intake in detail over periods of weeks. Subtract my exercise and some other activity, and that easily puts an upper bound on my BMR of 2000kcal/day, most likely more like 1800. A lot of kids freak out when they see those numbers, because they've looked at stories about steroid filled freaks of nature that eat 5000kcal+ a day and think you couldn't possibly add muscle at my intake...
Schwarzenegger during his career as a bodybuilder was about my current weight when competing several seasons (he was heavier when he was a power lifter), but he probably had another approx. 15kg of lean body mass where I still have excess fat (if only I could magically transform my stomach fat and shift it to my chest and arms..).
That pretty much bounds the lean body mass difference for someone at around my current weight to around 30kg. I'm sure you could find someone with less lean body mass than I had when I was untrained if you went looking for really sickly people, but I was weak; you couldn't find many with more than Arnold without bumping the body weight up)
It's fairly normal to estimate about 12kcal per kg of extra lean body mass. The difference between untrained me 10 years ago and trained me today then adds up to only about 180kcal. And between untrained me 10 years ago and Arnold, about 360kcal/day.
Of course that's not nothing - 360kcal is a small/medium meal if you're careful. But very few find themselves towards the top of that range, so a difference that large at the same weight is likely not common (I was totally untrained and extremely sedentary when I started training), and if you do, your exercise will tend to dwarf the difference in basal metabolic rate. E.g. one of my workouts burns in the 500kcal range; I end up burning about 200kcal more per day on average. A top level bodybuilder will spend 3-5 times as long in the gym as me every week, maybe more (and on top of that, you are highly unlikely to get remotely close to Arnold level physique without steroids). But note also that this is before secondary effects: When I exercise, I am generally more active outside of the gym because I feel more energetic. I'll be more inclined to walk to/from the train station instead of taking the bus, or take a walk during lunch hour.
You can certainly find "mass monsters" amongst steroid using body builders today that have lean body mass way above that (e.g. Ronnie Coleman), but they are few and far between, and again the amount of exercise you'd put in makes the BMR relatively irrelevant.