I find I use conda first simply because it installs the binary, than try pip if the package isn’t there. For instance psycopg2 is far easier to install in conda than pip.
https://jakevdp.github.io/blog/2016/08/25/conda-myths-and-misconceptions/
Pip, which stands for Pip Installs Packages, is Python’s officially-sanctioned package manager, and is most commonly used to install packages published on the Python Package Index (PyPI). Both pip and PyPI are governed and supported by the Python Packaging Authority (PyPA).
In short, pip is a general-purpose manager for Python packages; conda is a language-agnostic cross-platform environment manager. For the user, the most salient distinction is probably this: pip installs python packages within any environment; conda installs any package within conda environments. If all you are doing is installing Python packages within an isolated environment, conda and pip+virtualenv are mostly interchangeable, modulo some difference in dependency handling and package availability. By isolated environment I mean a conda-env or virtualenv, in which you can install packages without modifying your system Python installation.
If we focus on just installation of Python packages, conda and pip serve different audiences and different purposes. If you want to, say, manage Python packages within an existing system Python installation, conda can’t help you: by design, it can only install packages within conda environments. If you want to, say, work with the many Python packages which rely on external dependencies (NumPy, SciPy, and Matplotlib are common examples), while tracking those dependencies in a meaningful way, pip can’t help you: by design, it manages Python packages and only Python packages.
Conda and pip are not competitors, but rather tools focused on different groups of users and patterns of use.