On the other hand, while The New York Times gets chastised here as liberally biased, the Washington Post is listed as neutral, whereas I see the reverse as being the case.
The biggest difference between them and Breitbart is the subtlty - they do a good job looking smart and give lip service to opposing viewpoints. They also have much better reporters, designers and editors. All that actually serves to make their bias more dangerous though.
To your second point, though, I don't feel too manipulated by them precisely because I don't seek them out to confirm my own bias, but instead because of the high quality reporting. I admit that I only read The Guardian for the occasional book review, but I singled out the Washington Post in contrast to the NYT for its shameful clickbait tactics. I would easily read the Wall Street Journal over the Washington Post.
I haven't read enough Breitbart to know if it would be fair to call them a right wing version of the NYT in some loose sense, but it's not like they are winning Pulitzers with original reporting. Unlike the NYT, I'm not sure that you'd find much high quality, original reporting if you filtered out the slant. I admit I could be totally wrong here, but I always assumed that Breitbart was more of a right wing blog akin to DailyKos, than an actual newspaper (despite being presented as one).
I hope that's something that can be fixed though, because I do love the idea of this site...