In my experience, the line out and headphone out can have different results and can make for an unfair comparison.
I remember that when I did a HM-801 and DX-100 comparative review (in Portuguese
here, but I guess Google Translate might do a reasonable job), I tried using them in every possible configuration. Keep in mind that in the next sentences I'll be talking about considerably small but noticeable differences.
As a stand-alone player, the HM-801 sounded warmer and more mid-centric, while the DX100 was colder, with more present treble and bass but the midrange sounded relatively congested and less transparent than the HM-801's even though tonally it may well have been more correct. However, when I plugged both units in my old Meier Eartube using them as sources (transport + DACs), the differences were more noticeable and changed the results quite a bit. The DX100 went a few steps ahead of the HiFiMAN, as the sound opened up and it sounded very transparent, clear, linear and balanced. The HM-801, meanwhile, presented a clearer and more impactful sound but was, when compared to the iBasso, the one that sounded congested and the somewhat less competent tonal balance became more evident. I concluded that the iBasso must have been held by an amp that wasn't really on par with the DAC section, and was therefore the bottleneck of the player.
So my point is that when you connect both players to an external amplifier, you are bypassing a very important piece of it, which may have considerable influence on its performance as a standalone DAP – which is how most people will use them. So the HM-801 may have a better DAC than the FiiO, and that's what you heard in your comparison, but as players, using their respective amp sections, you may find that they're in fact closer. Maybe the FiiO can even take the lead in the amp section and surpass the HiFiMAN, I don't know...
All I'm saying is that maybe this isn't the best way of conducting this test!