Except the NYT and Wapo have a much better history of correcting mistakes. Comparing Daily Mail and NY Post to other serious news organizations is really an apple to oranges comparison.
Have a look at the list of "reliable sources" as defined by Wikipedia [1] and decide for yourself whether there is an unbalance between the number of green (which translates to "reliable") "progressive" and "conservative" publications.
[1] https://en.wikipedia.org/wiki/Wikipedia:Reliable_sources/Per...