Compared to the old site, there's a lot of "big text", too much of a focus on images (when you drill down into the site) and less on text, and low information density.
Worst of all (for me) - when loading on latest stable Chrome on Android, with a very fast internet connection, the page appears loaded but as soon as I scroll a number of the images disappear and the layout changes. I have to scroll back to where I wanted to be. Lots of scripts, client-side rendering, etc. It's overkill for a site whose focus should be content, not interaction.
While I'm sure the team built a technically impressive website, I don't think they've built the "right thing" and I certainly don't think it's better than the old one (from a user perspective).
But both these sites still suffer from "the flash", where it renders once, and then renders again half a second lafer with everything moving. It's disorientating and simply a bad UX.
Also the BBC used yo have this terrible experience for a few months where it would flash up a load of code, but they finally seem to have fixed that.
IMO both these sites are presently advertising that the responsive trend sucks ass.
I have started to realise that compared to the desktop sites it's almost impossible to get information out of these mobile sites at anywhere near the speed or information density I previously used to simply using the built in pinch and zoom and desktop layouts.
Like you scan broadsheets and desktop layouts, but the mobile you get a big, useless picture and a story title.
In particular, 'the flash' you mentioned on The Guardian means that often, instead of iOS 8 Safari scrolling when I try to scroll, it activates a link - or worse, an ad! It's infuriating, and it's significantly less usable than their old site in that regard.
For a truly bad mobile site, though, try going to Cricinfo: http://www.espncricinfo.com/ Go to an article, then go back. Notice that:
1) Your horizontal scroll position in the article list is lost.
2) The page renders, then re-renders exactly the same (for me at least), with a jump to the top of the page in between.