These two figures tell different stories. The difference between them is that non-wage non-salary benefits--overwhelmingly health and pension--are included in the second and not in the first.
From the perspective of workers who are not part of the salaried part of the upper middle class--for whom benefits are, we think, a large part of compensation--the first diagram is more relevant. It shows (a) the explosion of the wage-and-salary share during the late 1960s, (b) the rollback during the 1970s and the further downward push of the wage share in the early 1980s, (c) constancy up until the late 1990s, (d) a wage-and-salary share boom during the "new economy" boom, and (e) the collapse of the wage-and-salary share since 2000.
From the perspective of the salaried part of the upper middle class (or of the declining fraction of other workers with ample benefits) the second diagram is more relevant. It shows (a) the explosion in the labor share of income in the late 1960s, (b) continued rise through the 1970s, (c) a rollback during the early 1980s, (d) a decline in the labor share and then a recovery in the Clinton years, and (e) nothing terribly unusual for the state of the business cycle going on since 2000.
I find this frustrating. The national income accounting tells us that what is going on with benefits and their distribution has a profound effect on how we understand the recent economic history of the distribution of income between labor and capital, and I don't think I have a good grasp of what is going on with benefits and their distribution.