I have built a number of the two transistor “Joule Thief type” V boost circuits, and they work okay. I am comparing the two typical types: the PNP – NPN and the NPN – NPN types. The common one is the PNP – NPN type which uses a PNP transistor for the first transistor and a NPN type for the second transistor. With the collector of the first transistor driving the base of the second transistor, there is no need for the pull up resistor needed in the NPN – NPN type.
Not only does it eliminate one resistor. The PNP – NPN type also drives the second transistor with as much current as it needs, where the NPN – NPN type needs to have a low value resistor to supply enough current to the second transistor’s base to keep it in saturation, AKA fully turned on.