Does pip allow version number dependencies? Conda is able to upgrade/downgrade packages to resolve conflicts, whereas pip just seems to check if a package exists and shrugs when there's a version conflict.
pip does handle versioned dependencies and ranges, and know enough to upgrade existing packages when needed to resolve an upgrade. Its resolver isn't currently as complete as Conda's - see https://github.com/pypa/pip/issues/988 . (On the other hand, the fact that Conda uses a real constraint solver has apparently been causing trouble at my day job when it gets stuck exploring some area of the solution space and doesn't install your packages.... so for both pip and conda you're probably better off not relying too hard on dependency resolution and specifying the versions of as many things as you can.)