I do not know why they used a 308 in the original design, instead of another 301A, but an OP27 is much faster than a 308 and will require external frequency compensation changes. The lower noise of the OP27 is not a benefit because even a low noise reference will determine the output noise. My guess is that at the time, the 308 had better precision than a common operational amplifier and was more easily available without a high price.
The LT1008, LT1012, and LT1097 are superior replacements for the 308 with similar dynamic performance, but a cheap OP07 should be almost as good. The LT1008 is an exact replacement including compensation, while the LT1012 and LT1097 have intriguing support for overcompensation.
There are tons of suitable modern operational amplifiers though, except for replacing the 301A if clamping is used.
I like using this design as an example because it shows several things:
1. High side current sensing combined with an error amplifier. Note that this creates an output current error from the pass element base current, which was acceptable with the LM395 but probably not with bipolar output transistors. This could be corrected with a JFET or depletion mode MOSFET driver, or a MOSFET output.
2. Use of external compensation for clamping, which unfortunately is limited to the 301A, but at least they are still in production. The 301A also has a common mode input range which includes the positive supply.
3. Active pull-down of the output.
4. Compensation to allow for a minimum of output capacitance.