I wish I had a dollar for every time this question has been asked on various forums. I could probably buy a very decent set of headphones or loudspeakers with the proceeds. I could also cut off all discussion by stating this is a dumb question. Why is it a dumb question? Because it begs for a universal answer to a question that demands specifics to have any validity...Which headphone attached to which amp is more accurate than which pair of loudspeakers attached to which amp in what kind of listening environment?
Because audiophilia is all about specifics and details.
And even before you can get to the point of asking about specific components you've got to answer the question, "What is accuracy?" The simple answer could be, "the ability to transfer data with no loss of information." Or it could be "to not alter a signal in any way during processing." Or it could be, "garbage in, garbage out" depending on your source and signal chain.
Obviously audio engineers have an array of tools to analyze how transparent or accurate an audio system is. Some look at the signal in the electronic terms while others look at the acoustic wave generated at the end of the signal chain. All offer some way to quantify quality, but none will tell you if a system or component is "accurate" in absolute terms and all conditions.
There are probably thousands of plug-ins, filters, and EQs that are designed to alter the signal in some way. All, once employed, render the new output different and not accurate to the original input, but in these cases that is intentional. And in many cases the final result may be more euphonic or a better fit for a mix or playback situation.
But just because they sound "better" doesn't mean any are more accurate. Of course, once employed in a song's mix, the question then becomes does the rest of the signal chain render these intentional alterations accurately?
The standard and overly simplistic argument that headphones are more accurate stems from the fact that when listening through headphones the listening environment is not affected by the acoustic nature of the room you are listening in. With loudspeakers the room becomes almost an equal partner in sound transmission that has a marked effect on how a loudspeaker sounds. But this presumes that loudspeakers and headphones are both designed to produce a "flat frequency response" and that earphones have a more standard environment to operate in. That is not the case.
While a loudspeaker can be measured accurately over its entire frequency range in an anechoic chamber, earphones are not as straightforward to measure. First there is the issue of positioning - moving an earphone even a couple of millimeters in a test-ear jig can change the measurements. Also, there is no way to accurately predict the perceived frequency response of earphones above 8Khz range due to the vagaries and idiosyncrasies of each person's ear canals.
Another important issue in terms of judging "accuracy" is that most headphone manufacturers have their own in-house frequency curves that they aim for - some aim for "flat" while others go for a warmer sound. Some even purposely add bass - NAD and PSB's "room feel" curve is an example of this - the goal was to duplicate the bass added by the augmentation of the interaction of a loudspeaker with the room.
So, it seems that all transducers have serious issues that make it difficult to exactly quantify on any sort of absolute scale just how accurate they may be. OK, so we can't get there from here...
But you can judge two similar transducers in a controlled listening situation. Comparing two headphones or two pairs of loudspeakers to see which one is more accurate is something that any audiophile can do, given some well-known (to them) reference tracks and half-way rigorous test methodologies. But let's face it, for most music listeners "accurate" is not as important as "sounds good." And currently the vast majority of transducers can, if installed into a sympathetic set of components, sound good these days.
As to whether any particular transducer, be it an earphone of a loudspeaker, is "more accurate" than all its competition is something that many manufacturers aspire to, but when you look at the fundamental problems of each transducer and measurement technology in the end judging accuracy still comes down to "the lesser of two weevils" rather than an pinnacle of absolute 100% perfection.
And the answer to the original question was/is and always will be neither...