This is exactly my point: there is no *such a big* difference justifying the investment in the DAPs *or others phones*.
I tested personally the Cozoy, Chord Mojo, DragonFly Red, Oppo HA-2SE and FiiO X5 and also compared the iPhone with the Samsung S8 (EUR) and the HTC 10.
Just buy better IEM and/or try another music program as Onkyo HF or KaiserTone. Here you listen a difference.
I definitely agree on the IEM part, a great IEM/Headphone will almost always make a bigger difference than the source. That said, in some instances, a good source can make a world of difference and the value of items such as the Takt Pro cannot be diminished.
This is mainly due to output impedance for IEMs, which isn't super high but a few ohms on the iPhone dongle. If you have a low impedance, multi-driver IEM, the output impedance can drastically alter the earphone's sound. On the contrary, if you have something harder to drive, a decent power output (not just with regards to voltage/volume) will provide superior dampening, in turn, creating a more controlled bass response. This is the main reason why you see AMP reviews on Amazon where the user complains there is no bass. Rather, the bass is a lot tighter and more controlled where it may have been warmer, looser and the sound overall darker from a lower-powered source with a higher output impedance.
When you start comparing entry-level dedicated sources to high-end, then it can get more ambiguous but there are still clear objective and audible advantages of course, with diminishing returns. Still, kind of ridiculous to see users with a $1000 DAP and $100 IEM. Yes, cheap IEMs are terrific nowadays, but I doubt anyone would compare the iBasso IT01 favourably to the Campfire Audio Andromeda to name popular examples. On the contrary, the difference between the Fiio Q1 MKII and iBasso DX200, though substantial with a resolving IEM, isn't nearly as transformative as output impedance and power are already sufficient on the Fiio.