For a constant-current circuit it would be the dropout voltage plus the reference voltage which is often about 1.25V.Otherwise use an LDO....dropouts << 1V, plus you get short circuit and thermal protection.
The two-transistor circuit is protected against short duration shorts (since it limits at the constant-current), but its dissipation does need to be considered.you do get the low dropout at the expense of circuit protection -
For a 12V short @ 50mA that would be 600mW.