Decoherence on its own still has a basis problem. You need superselection to reduce that to one basis. However this has been shown long ago (1980s) so in essence decoherence + superselection does solve these problems.
If you're not familiar with these terms I can explain.
In general all these interpretations are more popular on the technically literate web going culture than in actual research in physics where Copenhagen style views still predominate.
For the simple reason that all of the other interpretations (Many Worlds, Bohmian, Transactional) only somewhat work with Non-Relativistic QM not with QFT. Only Copenhagen works with QFT.
Decoherence does not give you Many Worlds, or at least not unless you interpret it that way.
Decoherence or more strongly environmental super-selection from something like electromagnetic scattering, results in a Classical probability distribution over the macroscopic observables or more accurately renders the algebra of classical properties Boolean. This means there is no interference between the terms and the probabilities are simply ignorance of facts which have occurred.
Once this superselection process has occurred the mathematical structure of macroscopic observables is just as it is in classical statistical mechanics. There's no need to read this as multiple worlds, although you can if you want to. If interference terms persisted you might have more of a case for Many Worlds. Even then though there are other ways of reading the formalism.
If you're not familiar with these terms I can explain.