Linear regulator using emitter follower and operational amplifier
An emitter follower has a minimum voltage drop below the Vout of the op-amp of about 700mV. If the op-amp can be supplied with a higher supply voltage than input voltage you can reduce that to tens or hundreds of mV, which might be competitive. I have done this in a situation with +/- 8V rails and a 5.6V rail regulated down to 5V using an emitter follower, with the op-amp supplied from the 8V rail. Most commercial regulators do not have a separate supply pin for the internal circuitry so this is not an option. 

If you use a PNP or p-channel transistor rather than a follower the drop an be less, but ensuring stability is more difficult, as with commercial LDO regulator chips.

If you design your own you are free to use a better reference, a more accurate op-amp etc so you could get better performance. You might have a free op-amp out of a multiple package. 

Generally though, you will be better off using commercial parts in almost all situations.