There are obvious different use case scenarios for loudspeakers and headphones. And so the obvious thing to say is that you use such and such for this purpose, and so on for a different purpose. Jogging, walking, taking a piss, whatever.
But this being head-fi, derived from the term hi-fi, which stands for high fidelity - the actual question is, between loudspeakers and headphones, which of these reproduce sound of a higher fidelity than the other? Right now, the best loudspeaker setups trounce the best headphone setups for sonic fidelity and realism.
With the best possible loudspeaker setups, it is possible to be fooled into thinking that a musical performance is happening live, right there in front of you. Even mid to high end loudspeaker setups allow you to identify where the instruments are positioned, several feet in and around the loudspeakers.
The best possible headphone setups have gotten things like tone, timbre and presence to remarkably excellent levels. But the one thing that they all fail at right now is imaging and sound stage, which is only going to be at most an inch or two in and around the head.
It is an especially pertinent question for anyone who has just discovered the audiophile in themselves and is wondering which route to take, loudspeakers or headphones. After all, 'cost is no object' will be a foreign term for the vast majority of us - most of us will not be able to achieve extremely good fidelity in both our loudspeaker and headphone systems due to the great expense.
In my case, I fully understood the limitations of headphones but because I didn't have the space for a proper hifi system setup with loudspeakers and am still sickened by the cost of high end hifi gear - headphones are my only real option for enjoying the music, the pursuit and the high fidelity of sound reproduction.