That last post has an inconsistency.
When pushed to the high end, a BK indeed does not have an advantage in burn times - it can't create more BTUs to put in your room than those that were put in the firebox.
However, EITHER the times are the same between the BK and a non-cat with the same loading capacity and the same heat output (e.g. 3 cu ft and 40000 BTU per hour) OR the thermostat limits the heat output (a bit) below what the other stove can do, leading to (slightly) longer burn times for the BK at a (slightly) lower output in its high-end output range.
A "burn time will be the same but will not match the top end output" is simply incorrect, as it makes BTUs magically disappear somehow. Pounds of wood in -> BTUs per hour out for xx hours. No escaping the consistency of the math here.
Think of it this way: you have a firebox that you stuff with a number of pounds of wood, equaling a number of BTUs. The stove allows you a certain range of BTU output rates; high for when you need a lot of heat per hour (b/c of losses in the home) and low for when you don't.
The tunability of the stove is your control in how fast you want all those BTUs in the firebox released into your home.
(This all assumes the same efficiency, i.e. BTUs lost thru the chimney, between stoves - which is for all practical purposes the case when comparing modern stoves.)
The advantage of the BK as compared to many (though not all) is instead at lower burn times, as it is possible to decrease the BTU output per hour by a lot for BKs *while keeping your chimney clean* (one can always turn down the stove, but this may result in a smoldering mess in your stove, and then soon after that in your chimney, and if you're out of luck your home). Hence the advice to compare BTU output ranges, as that is what gives you the range of control.
The BK is unique in having a thermostat (well, I vaguely remember there is one other stove that has such a thermostat, so unique is too strong a word). While many others proclaim their stove provides even heat, I have as of yet to meet a BK owner that says "yeah, my previous stove was even, and this one too". No, those who move from another stove (cat or non-cat) to the thermostat controlled BK invariably laud its more even heat as compared to their previous ones. And this holds even more so at the low end, where rearranging fuel during a burn changes the wood surface area available for heat production, and thus changes the heat output if the air control does not compensate for that.
Finally, it is worth considering what you want: cover *all* heat needs in the worst day of winter, or carry your base load with wood heat and modulate with oil/propane/... on top. The latter evens out the temperature in your room already, so an even-output stove is not that advantageous there. Also, as noted elsewhere, low heat output (shoulder season) heating can be done cheaply and efficiently in other ways, e.g. a minisplit (or a minor oil/gas bill).
These are all choices, perspectives, and preferences one has to consider when trying to reach a satisfactory decision.