Single transistor level up shifter
The single-BJT level shifter in the question would work: If the input impedance of the device on the 5 Volt side is significantly higher than the 6.8 k shown in the question, the expected ~0.3 to ~5 Volt signal would be received (taking a 2n2222 as an example). 

However, for lower impedance inputs, the input would act as a voltage divider with the 6.8 k resistor, attenuating the high part of the signal significantly. 

For instance, if the input impedance of the load on the 5 Volt side were, say, 100 k, the signal would top out at around 4.6-4.7 Volts. Still not too bad. 

Any lower, and the level becomes problematic. This is when one needs an alternative, such as a two-transistor set-up mentioned in the question, to drive the output rail harder.