Well, picture two circles, partially overlapping one another. One circle represents all that is a Rocket Stove and the other represents all that is a Masonry Heater. They have areas of overlap, and areas which do not overlap. So the simple answer is both yes and no.
With regard to "better" there is no better until one defines the operating parameters and limitations of the environment. "Better" is whichever design best fits the full range of needs.
Having said that, I'll try to answer what I assume you mean.
The "Rocket Stove" is what I think of as the "engine" of what most of us call RMHs (Rocket Mass Heaters). It was originally a cook stove, not a heater. It is however, the origination of the basic geometry of the RHM. A short feed tube, short horizontal burn chamber, and a relatively tall fire riser. The feed tube and burn chamber have the effect of concentrating the heat and mixing fresh air with products of the burn, which continue to mix and burn up into the vertical fire riser. And it burns hot! I personally think temperatures of around 2,000 F is about right for a J-style RMH, with a few hundred degree plus/minus around that.
This extreme heat is good, because it burns the smoke and most of the other products of combustion. This results in a really clean burn. No creosote. No chimney fires. But we also have to strive to keep that heat where we want it, in the burn chamber and fire riser. So we insulate these portions of the firebox. And we insulate the firebox from nearby objects, structures, and usually the floor and room in which the RMH is built.
A Rocket Stove burns like this too, just like a Rocket Mass Heater (which I often call a Rocket Heater, because the Mass is really a different variable).
A Rocket Stove becomes a Rocket Heater -in my opinion- when we place the upside down barrel over the fire riser (in place of a pot of stew, as when used as a stove, instead of a heater). We then channel that hot air directly at the top of the (now inverted) barrel, and as the air falls down the side of the barrel it releases a lot of heat through the metal sides of the barrel. This gives us immediate heat into the surrounding area. The hot air then flows through a manifold area, and into whatever we have decide to do with the hot air from there on (this could be a bench for thermal storage, one or more bells, just out the chimney, or in rarer cases an alternate heating load).
If we decide to route the hot air through thermal mass, that mass will pick up some of the heat, and as the air surrounding that mass gets cooler, it radiates out into it. The greater the temperature difference, the more quickly this happens (the same is true of the heat getting sucked up into the thermal mass from the hot air). This is exactly what happens with a well designed masonry heater. For that matter, the rapid and hot burn is also exactly what happens with a well designed masonry heater.
In terms of overlap, the thermal mass used to store the heat generated by the fire employs exactly the same physics. The routing of the heated air may or may not be the same as used in traditional masonry heaters. However, the configuration of the firebox is very different in a RMH than in a traditional masonry heater. (Better in many if not most cases, it seems to me.)
Now, add this this, there is a second type of RMH, called the batch box. Peter VDB has done a great deal of work on this, and really gotten a nice system designed. It is even closer to a traditional masonry heater than the J-style RMH, because the J-style needs someone to poke at it and play with the sticks every few minutes. But the batch box is very similar to a traditional masonry heater because you load it up with a charge of wood, and 45-minutes or so later that is all burned down the coals.
Which is "better"? I don't know how to answer that, other than to say it depends upon what you want, how you want to burn, and what kind of heating you need to supply.
Personally, I am better suited to a batch box design. I don't really like fiddling with the burning sticks every few minutes. I'd much rather start the fire and do something else and leave the fire to attend to itself. So that's the first operational choice I think one has to think about. Depending upon your answer to the "fiddling" aspect, you'll likely favor one or the other.
Then it is a matter of sizing the thermal mass to your heat load, and deciding how you want to capture the heat in the thermal mass. I may yet change my mind, but I have begun to lean toward a standard batch box barrel design, married to a double bell bench concept. But I still might just make the more traditional cob bench too. I'm still playing pros and cons in my mind. And cost and materials plays a big role too. If I can do one more cost effectively than the other, I may well implement that design simply for economic reasons.
That's my two-cents. I'll be interested to see what others think.
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