Size
Not trying to start a big discussion here, but...
I see that statement used on this forum often, and it ain't quite correct. Where it goes wrong is with the word "heat" instead of "energy". Einstein's famous equation E=MC[SUP]2[/SUP] states that any substances of equal mass contain the same stored energy, not heat. Mass is not the same thing as weight... for example, a square yard of concrete weighs less on the moon than it does on earth. Still, if we remain on earth, weight can be used to compare mass... on earth a pound of feathers have the same mass as a pound of steel, and both contain the same amount of stored energy.
When we burn wood we are using a chemical reaction to convert wood into something else, and that reaction releases some of that stored energy in the form of heat. Because a pound of cottonwood has the same mass as a pound of oak, if we could burn both, and trap all the heat energy released from both, it would be the same (in other words, if we had a 100-percent efficient appliance). But there ain't any such thing as a 100-percent efficient wood-burning appliance. A less-dense substance burns faster, or releases its energy faster... which means in a less than 100-percent efficient appliance a larger percentage of the heat energy will necessarily have to go out the flue.
Think of it this way... A pound of toilet paper holds the same stored energy as a pound of oak. For illustration purposes we will unroll that pound of toilet paper so it lays loose (even less dense). Now, take two wood stoves, put that pound of loose toilet paper in one and a pound of oak in the other... light them both. In just a few seconds the toilet paper will be consumed by fire in a massive hot flame, but you can lay your hand on the stove because near none of it was transferred to the steel. The oak is just getting started, and in a few minutes you won't be able to touch the stove without receiving a nasty burn.
It's the same thing, at a considerably lesser degree, with a less-dense wood; A somewhat smaller percentage of the heat produced will be available, or harnessed, to warm your butt. So even though a pound of cottonwood has the same potential heat value as a pound of oak, you would need a 100-percent efficient appliance to realize it. A high efficiency burn will do a better job of harnessing the heat from cottonwood... but at the same time it also does a better job of harnessing the heat from oak, although the gap gets smaller as efficiency increases.
But in the end, no matter how you slice it, you will harness more heat from a denser wood... you will get more heat from a pound of oak than you will from a pound of cottonwood.
I adjust my heat with size of piece that goes into the stove. I am just going to disagree with you on your last statement. Yes, if you split to the same size, different species will throw less or more heat "by the chunk", but if you split and burn with a bit more thought, using a much larger variety of sizes, plus adjust your stove feeding schedule appropriately, you can use the lesser species just as efficiently and it doesn't get into the ridiculoous range either.
Example, I burn a lot of the lesser tulip poplar and sweetgum. They are still great firewood sources, easy to harvest, and we have them in plenty. I adjust what size, how many, and frequency of loads determined by what demand I need any particular day or time of day, as the needs change all the time. I stack a really LARGE variety of sizes and species. No way are my stacks uniform in chunk size. This allows me *huge* flexibility in burn, and also what I can use from the woodlot again, huge flexibility.
My old heater is designed in such a way as it will throw heat with a single small stick, or filling it up, or anything in between, with whatever ya got, all you have to do is think about it, what you are trying to do. It is both a front and also top loader. Loading from the top I can put in quite a large chunk for a room heater type heater, or pack it with smaller rounds and splits (very rarely needed here, but it could be done if demand warranted it). On lesser demand times, load from the front, one or more pieces at a time. I even can time the heat output, say I want a little heat, then following that more heat, as in early evening to later on. Lesser species go on the bottom, throw a chunk or two of oak or whatever on top, it burns good that way and you can feel the heat output go up as soon as the bottom wood is mostly gone and the oak gets going later.
It's all in how you size and use your wood. There's a place for the lesser species in most scenarios.
And I burned the same way when I lived in New England, with plenty of double digits below zero temps to deal with, so it is not exactly a function of living up north and having a big heat demand for extended times, I still burned lesser species up there, and it worked fine. I like the "multifuel" method over the "just one species and one size" perfect wood approach.
Now I don't own or run any expensive EPA stove or boiler, so perhaps it is different, I will readily concede the point as I have no experience there, my only experiences are a variety over the years of plain jane old wood (cook) stoves and room heaters and some indoor plain furnaces, no water heating, just plain hot air. But, with those heaters, paying attention to load size and species versus demand and output desired is just as scientific a way to go about it as any other way, plus it results in cheaper and easier wood harvest, as you can take most anything and make good use from it.
Now ideally, a wood combustible appliance would be using very uniform fuel, such as pellets, with automatic controls, etc., to get the greatest efficiency, but once you start talking about harvesting your own and using various chunks of wood, efven similar size and the same species, then you just have to think a lot more, and it takes a bit more skull sweat to achieve close to that level efficiency. But, it can be done.
Beyond that, it would probably be better to build a pure designed wood gasifier and burn the gas in a real gas heater, if you really wanted maximum efficiency. I know the various designs of wood heaters I have seen posted here attempt to hit at that level, but there are pure gasifiers that work better.
I never have built one, although I did build and burn (test burns) a methane digester before. A wood gasifier would be interesting as you could run a cheap generator as well from the output, along with your heat. You need serious gas scrubbing though and like stainless steel plumbing and all sorts of expensive stuff.
different discussion sometime.