Lots of threads on this. It depends what you're looking for -- if you're happy with your unprocessed tone and just want some more girth, fattening, what-have-you, this means you want something transparent, which (IME) the Blueberry is not. It has a boost going on in the mids that I was never able to dial completely out. If that doesn't bother you, it is otherwise a great pedal. For transparent OD's, the Grizzly is by far the most versatile one I've tried and can vouch for what @Fuzzbass says. The Blueberry does not approach the Grizzly's capabilities at higher gains. Others will vouch for the Smallsound/Bigsound Mini, which is also supposed to be quite transparent and able to cover a wide range of gain.
I can't speak for the Azure Drive, but from what correspondence I've had with Josh and what others say, it sounds like a terrific pedal -- from the man himself, responding to a question I had about its transparancy:
"Yeah the Azure Drive can get the Blueberry sounds but I made it capable of being much clearer. I would say it is more transparent than the Blueberry, but can also get more extreme in the gain settings. The tone control is more intuitive; it is a simple boost/cut of treble, rather than a low end boost/fuzz like on the original."
If all you want is a transparent low gain pedal, the Barbershop is a great option. I have one and have been using it as my always-on low gain OD for a couple of months (the Grizzly handles the high gain for me). Because I am an inveterate tinkerer, however, I also picked up a TC Spark Booster, which I'm testing against the Barbershop in the always-on role. Difficult to say yet which I like more from a tone standpoint, but one thing I like about the Spark is the bass and treble knobs, which give me some more flexibility at my feet. It's also about half the price of a Barbershop, so there's that.
If transparancy isn't a priority for you, I can't really provide much input --you just have to try a bunch out to see what you like. There are literally hundreds (thousands?) of options. A Source Audio Aftershock might be a good route that would allow you to try a bunch of different sounds without dropping tons of cash on pedals -- I just grabbed one for precisely this reason. It's digital, but early reports are glowing.