One can easily have both headphones and a speaker system, and they are meant for enjoying the music in different settings, so the debate about which is better is kind of moot.
For musical enjoyment, one doesn't need 6 figure speakers to compete with reference headphones. Indeed the sound stage and physicality is better with speakers, and around 3000 euros one can get a good enough pair of speakers, see my examples a few pages back.
With both headphones and speakers, both objective and subjective methods are relevant. Objective methods set the minimum requirements, but our hearing is more refined than instruments in judging musicality. Correlation between objective and subjective is always what drives objective methods forward. For instance there is a huge literature about nonlinear distortions that are just being picked up by industry, for a next jump in where to focus to get most musicality out of a given budget.
For musical enjoyment, one doesn't need 6 figure speakers to compete with reference headphones. Indeed the sound stage and physicality is better with speakers, and around 3000 euros one can get a good enough pair of speakers, see my examples a few pages back.
With both headphones and speakers, both objective and subjective methods are relevant. Objective methods set the minimum requirements, but our hearing is more refined than instruments in judging musicality. Correlation between objective and subjective is always what drives objective methods forward. For instance there is a huge literature about nonlinear distortions that are just being picked up by industry, for a next jump in where to focus to get most musicality out of a given budget.