Portable DAC and Iphone

I would like to be able to get decent music out of my iPhone for headphones and perhaps putting in my system.

However, from what I read on at least one review was that the iPhone sucks and adding in say a Audioquest’s DragonFly only makes it suck a teensy weensy bit less.

Perhaps a Chord Mojo would be better?  In that case though it is pretty expensive and large for listening while mobile and then I wonder if that is wasteful and I should just get an amp or separate DAC solution and say screw it to portable.

Thanks Greg and I will check out the Sony.  One thing I did see on the web that differs from you experience was a test on the new iPhone 7 dongle.  

Measurements show it to be inferior to the headphone jack only iPhone 6+

“The results are clear: with an iPhone 6S, the dynamic range worsens by 4.5 dB(A) for 24-bit music files. For the iPad Air, it worsens by 3.8 dB(A). The signal also gets worse for 16-bit music files, even if they aren’t that drastic: the dynamic range worsens by 1.8 dB(A) and 3.1 dB(A) for the iPhone and iPad, respectively."

I appreciate the input everyone.  I have some homework to do.

I do think that a very good set of headphones will help regardless.  It’s just how much more the DAC will improve things.
Yesterday I ordered some new over ear headphones on a whim.  I had some pretty mediocre pair but yesterday I tweeked the plug and now they are dead.

These are what I got. https://www.amazon.com/Philips-SHP9500-Precision-Over-ear-Headphones/dp/B00ENMK1DW/ref=sr_1_1?s=elec..

I got them at Newegg for $55 and for that money they are worth trying.

So I getting a DAC may be priority one now.  Does anyone have experience with the FiiO E10K USB DAC?