jetsam
Minister of Fire
I don't think all mass heaters are created equal and I highly doubt a "light" mass heater will be any more efficient than a freestanding woodstove.
Those popular diy mass heaters with no reburn must spend most of their time exhausting heated air out of the envelope. Probably nice to sit on, probably a net heat loss for the house unless you feed it constantly, or provide a way to block the air intake.
A simple snug firebox door would fix that, though it never seems to be part of the designs you see for them.
On the flip side of that argument, you can go on YouTube right now and see poorly insulated houses in Russia that were built around smaller masonry heaters and use them as the only heat source (though they mostly seem to feature some kind of multi-door air system that leaks some degree of combustion air into the house, according to the soot marks).