A statement of the quantum turbulence problem in both a Bose – Einstein condensate (BEC) and superfluid helium is formulated. In superfluid helium use is made of a so-called vortex filament method, in which quantum vortices are represented by string-like objects, i.e. vortex lines. The dynamics of the vortex lines is determined by deterministic equations of motion, supplemented by random reconnections. Unlike He II, the laws of the dynamics of quantum vortices in BEC are based on the nonlinear Schrödinger equation. This makes it possible to obtain a microscopic description of the collision of vortices, the structure of a vortex filament, etc. A comparative analysis of these complementary approaches is carried out. It is shown that there are some features that do not automatically transfer the results obtained for BEC to vortices in He II and vice versa.