Let's have some terminology: as far as I'm concerned, you can't be an atheist at all unless you believe there are no gods (not even one). It's not enough to not believe in God/gods--or we're going to have to call my cats atheists. So that's what all atheists have in common: they see the universe as being deity-free. They are the opposite of theists, who think the universe includes a deity (or two, or three...).
Beyond this common ground, atheists can disagree with each other, and even disagree about religion. By religion I don't mean bare bones belief or disbelief, I mean practices, rituals, a whole constellation of attitudes and activities. Some atheists are anti-religion, some neutral about religion, some even pro-religion. Back in the 20th century, before the "new atheists" came along, I knew both anti-religious and pro-religious atheists. One friend was forever railing against the silliness of Christianity (anti). A teacher was both adamantly atheist and sending his Jewish children to religious school (pro). So if you take "new" literally (and make the inception of "new atheism" coincide with Sam Harris's book The End of Faith), then old/new isn't really the distinction we need. How about, instead, hard vs. soft?
Hard atheists believe that religion is on the whole a bad thing, and wish it would go away, and may even actively work towards its demise. They think of religion as being like, maybe, crime, or disease, things that are essentially bad even if you can find an occasional good crime (stealing drugs for ailing children) or good disease (Lance Armstrong says cancer is the best thing that ever happened to him). They tirelessly make their case against religion by talking about pedophile priests, brainwashed children, suicide bombers, sexism, etc.
Soft atheists believe that religion is not on the whole bad, and don't have the same desire for it to disappear. They think of religion as being like, perhaps, sport. Sport is premised on some dubious attitudes--competitiveness, the notion that there are winners and losers; bad attitudes like team spirit--bad because that sort of partiality is irrational. Vast amounts of money and time are poured into sport at school, amateur, and professional levels--money that could be spent on much worthier things like alleviating poverty and disease. You can see all that accurately, and yet not be on the whole anti-sport, because you see both the bad and the good in sport. Soft atheists likewise see both bad and good in religion, and don't feel, on the whole, opposed to religion.
So, who are the real atheists? Hard atheists are the ones most in the public eye, thanks to the high profile of the "new atheists" ... who are mostly hard, most of the time. So to the public they are the real atheists. I think hard atheists see themselves that way. When they are criticized by soft atheists, they regard the latter as traitors, apostates, quislings,"faithiests." On the other hand, they don't see themselves as traitors (etc) when they criticize soft atheists. Hard atheists have "the essential position" in their own minds, and soft atheists aren't true believers--or rather, true unbelievers.
But why is hard atheism "the essential position"? Whether God exists is one question, the value of religion is a completely separate question. How can religion be valuable if so much about it is problematic? Think sports.