Besides its unusually low input bias current, the 308 was the choice for precision during the 301A/741 era before dedicated precision amplifiers became available and inexpensive. Sometimes users graded them for offset voltage drift or used them with an oven.
The LM308A was used in the 731B among others, it isn't the lowest in noise but not bad, a LT1012 would be a good upgrade.
And the LT1008 is a direct upgrade of the LM308. The LT1012 and LT1097 are the same parts with some pinout and function differences.
The input bias current of the original LM308 (1.5nA typical) which lacks input bias current compensation is actually high enough that modern precision parts like the LT1001 and OP-07 would likely perform better due to lower noise and even better precision. Just watch out for pinout differences in compensation and nulling.