The Gray Lady's Misleading Headline
The problem is that Reagan did not become president until January 1981, and his tax policy was not fully implemented until a couple of years later (and arguably not until his second term, when we got very significant tax reform). So the headline should have read, "Complaints Aside, Most Face Lower Tax Burden Than in Carter's 1980." That makes the story very different, as 1980 was the year the incumbent Carter was defeated by the challenger Reagan, who was proposing significant tax reduction as a key part of his campaign.
By the way, the online version of The Times omits the mention of Reagan in the headline. There, the headline is the more accurate "Complaints Aside, Most Face Lower Tax Burden Than in 1980."
Addendum: Using the Times online interactive graphic, you can compare the average tax rates between any two years. Here, by income level, is how the average tax rate changed from 1988, Reagan's last year in office, to 2010, the most recent year available.
0 to 25K, fell by 4 percentage points
25 to 50K, fell by 3 percentage points
50 to 75K, fell by 2 percentage points
75 to 100K, fell by 2 percentage point
100 to 125K, fell by 1 percentage point
125 to 150K, fell by 1 percentage point
150 to 200K, unchanged
200 to 350K, rose by 2 percentage point
350K+, rose by 1 percentage point
That is, according to the Times numbers, since Reagan left office, tax rates have risen at the top and fallen for the middle class and especially the poor.