With both civs running 2 scientists as soon as they have universities up and no other modifiers to the number of GS points, it'd take Korea 17 turns for that first GS and only 12 turns for Babylon.
Babylon's science specialists generate 95.76 beakers (72 + 33% bonus from University) in the 12 turns generate it's 2nd GS.
Korea's science specialists generate 159.6 beakers (120 + 33% bonus from University) in those same 12 turns.
Here's the catch. If Korea bought a library while building the Great library as well, both civs beelined Education before getting any other techs, didn't get a free tech from a ruins, Korea would get a could get 2 RA's worth of boost on top of the free tech from the GL. Let's say the tech order for both went Pottery, Writing, Animal Husbandry, Trapping, Calender, Philosophy with the timing such that the GL gives Civil Service, Theology, Education. Let's also say they both finish Philosophy 1 turn before the GL finishes and Korea buys a library for the tech boost. That would put the boost at the median value of (Sailing+The Wheel)/2*.5, which is (55+55)/2*.5 = 110/2*.5 = 55*.5 = 27.5 beaker bonus into Theology from the library and another 27.5 beakers into Theology from the GL's boost the next turn. That's a total of 20% of Theology finished from the bonuses. Therefore Korea should be able to finish education at least 1-2 turns before Babylon, if Babylon doesn't use its free GS to build an Academy nor to bulb Education.
Now let's say Korea did get to education 2 turns before Babylon, because of the boosts mentioned previously and both civs had enough cash to buy the University as soon as it is unlocked. Then by the time Babylon generates a GS from running 2 scientist Korea would have generated 14 turns of of beakers from its specialists instead of only 12 turns. That's 140*1.33 = 186.2 beakers or 90.44 more beakers than Babylon. On top of that Korea got another boost from buying the University. Since no other techs were researched at this point, the median would be between Sailing and Archery since Mining, Archery, Sailing and The Wheel are the only available techs to research. That makes the median value (55+35)/2*.5 = 22.5 or 40.9% of sailing completed.
Now if both civs beeline to Astronomy after education, by the time Babylon generates a GS Korea will have generated enough extra beakers from the specialists and the boost 22.5 boost buying the University gave to have 18% of compass researched. While Babylon's extra beakers would only get them to 47.9% of Optics.
Since it'll take Korea 17 turns to generate a GS and they have a 2 turn head start in this example, they're 1st generated GS would come 3 turns after Babylon's 1st generated GS. That's an additional 39.9 beakers for Korea and 23.94 for Babylon. So Babylon would have another 28% into Optics while Korea would have another 10.6% into Compass.
Yes I realize this isn't counting the beakers from population size, because I'm basing this off both civs having just 1 city and equal population and growth rates. In other words, I'm only comparing the bonus beakers each civ would earn in this time frame from a single university. I know I also did not count the bonus GS points from the GL.
Now let's look at both civs having built a total of 4 cities all with a university running 2 scientist each and we're at the point where Babylon just generated its 2nd GS, so the cost of the next one is 300 GPP. For argument's sake we'll say the University in the 2-4th cites just finished, so all 4 cities have 0 GS points built up. Just from the GS points the specialist generate it would take 34 turns to generate the next GS.
Babylon: 34 turns with 8 scientists generating 3 beakers each multiplied by the 33% bonus from the university comes to a total of 1085.28 bonus beakers.
Korea: 34 turns with 8 scientists generating 5 beakers each multiplied by the 33% bonus from the university comes to a total of 1808.8 bonus beakers.
Korea generates 723.52 more bonus beakers than Babylon over those 34 turns.
If at this point both civs have the Rationalism policies for +2 beakers per specialist and to make the University give +50% instead of +33% here's how much the differences become.
Babylon: 34 turns with 8 scientists generating 5 beakers each multiplied by the 50% bonus from the university comes to a total of 2040 bonus beakers.
Korea: 34 turns with 8 scientists generating 7 beakers each multiplied by the 50% bonus from the university comes to a total of 2856 bonus beakers.
Korea Generates 816 more bonus beakers than Babylon over those 34 turns.
Conclusion:
If both civs sign the same number of RAs on the same turn, the bonuses Korea gets from running specialists and the RA like bonus from the science buildings built in the capital, both civs save all their GSs for the last techs needed to win the game and both civs have the same number of built cities and puppets, Korea should be at least 3-4 techs ahead of Babylon when they start using the GS's to bulb, in part because by the time they build/buy the public school and research lab in the capital, they should have both the porcelain tower and rationalism opener, making those boosts worth an extra median tech each . This tech lead from the boosts and bonus beakers also means Korea will have the University, Public School and Research Lab built/bought in its cities before Babylon unlocks those buildings. Thus, even though Babylon get's a 50% bonus to GS generation and the free one at Writing, Korea can get all their science specialists in sooner, thus increasing the bonus beaker gap and getting their fewer GS's sooner. Therefore, Korea could, theoretically beat Babylon to a science victory since their bonus beakers and tech boosts from buildings should more than make up for only generating 2/3 the number of GSs.
