The Retrosheet site can tell you the league averages for various situations going back to 1952 for the NL and 1953 for the AL (plus some earlier years). Here I show the league differences in close and late (CL) situations for both batting average and isolated power. Each league is done separately and each data point is a 3 year average (just a simple average, with the exception being that the first AL data point is just 1953-4).
The first graph shows the NL AVG difference. That was calculated by the non-CL situations minus the CL situations. For example, in the NL in 1952, the non-CL AVG was .251 while the CL AVG was .248, for a difference of about .003. The next two years had differences of about 0.007 and 0.008, respectively. So the first NL data point was (.003 + .007 +.008)/3 or .006.
Notice how the difference is growing over time. This might be due to the greater specialization of relief pitching. But that is just a guess (although the correlation between the 3 year AVG difference and the % of games not completed is .74 in the NL-it was also about .74 for ISO-in the AL those correlations were .85 & .93, respectively-the last graph shows NONCL ISO MINUS CL ISO AS A FUNCTION OF GAMES NOT COMPLETED IN THE AL). Now the same graph but for isolated power (or SLG - AVG).
I wish I could explain what was going on in the late 1960s and early 1970s. It does not seem like it was that much harder to hit in CL situations than non-CL situations in the NL. Now the AL graphs.
The graph below shows how closely related the difference between clutch and non-clutch hitting is to the % of games not completed. The fewer games completed (the more relievers are used), the harder it is for hitters to keep up their normal power hitting in close and late games.