In my field (science) Anaconda is probably the most common Python distribution in use. conda is the package manager (just to be clear of the distinction).
It is difficult to find fault in conda when compared with pip+virtualenv.
The one point that I would make is that the Anaconda distribution is meant to be installed per user. If you have a Python environment that is shared across users there is no way of doing the equivalent of
pip install --user with conda (but read on for a surprising solution...). Nor users can create conda environments.
So, if you are considering a single user installation go ahead and try Anaconda. It is worth a try
Note that you can use pip with Anaconda... they are not incompatible. In fact that can be quite useful in a shared installation.
I have setup a shared-user conda installation where users can install user-space packages with...
pip install --user.
In a shared installation I do not see how users can create their own conda environments (conda has environments). And I bet conda+virtualenv would be a mess.
Note that conda is not Python tied: First you can have a conda installation with both Python 2 and 3 - and conda manages environments very well. But you can also have conda install Perl, R. In fact that is quite common. Our Perl interpreter is provided by Anaconda ;)
Also I suspect conda is probably stronger in Linux and Mac OSes. Windows is less well supported. For other operating systems, there are probably no packages (or they will be limited).