That's a terrible reason to pick a design. If you have no justification for a design other than 'lots of other new websites do this', then you have no justification at all... unless your purpose is to blend in and be forgotten.
Personally, I find the new design conveys a more relaxing experience although I'd like to see some of the fonts grow a bit. By modern, I refer to a different online world than #000 against #FFF and skeuo approaches. I'm not saying, those days are over completely, but fresher approaches are nice too.
Let's face it - design will continue to morph based upon different philosophies and whims, just as fashion does. Some visions are worse than others but some are implemented in pretty clever ways. I like the way DDG went with theirs.
For a modern web property or search engine competing against the likes of Google, what timdiggerm mentioned in a reply nails it. Sticking with an older design philosophy conveys a negative image for many users.
However, other properties going flat and subdued do not necessarily get my attention just because everyone else is doing it. This one does though because they did a lot of things right. The more I use next.duckduckgo.com the more I appreciate the small details that were thought out.
I've been mostly against flat design for a number of reasons but IMO, you've achieved a great design. I really like the minimalism of the hamburger button. Again, everything just gets out of your way.
Perhaps enlarging the font-size of the search result snippets might help with the contrast complaints - personally, I like your use of the grays. Again, it conveys a modern design.
I really hope that there will be an updated iOS app soon too :)