The joker in this deck is the HD650. I have the HD-6xx which is essentially the same headphone. Many of us in the forum have one of them or the HD600 or perhaps the HD 660. All of which have certain similarities.
The HD-650 in particular is notable for scaling. Unlike many headphones to a large extent it will really sound better with better components, both DAC and AMP. Now it’s not going to suddenly sound like a $1500 headphone, but unlike many it will often improve remarkably with a better chain. Use the forum’s search function for Sennheiser HD 600 or HD 6xx and scaling.
These headphones are often kept around as they are good enough and common enough that many headphone guys use it as sort of a benchmark. We all know what it sounds like.
Now these 600 series Sennheisers are 300 Ohm headphones. They are harder to drive than most headphones - the most common being 32 ohm. Yes, you can have a dongle that makes them LOUD, but more power drives them more cleanly. Bass lines that had been muddy become crisp. To some extent it depends on your ears and how carefully you listen. There’s a reason that some use them for mastering.
The limitation of the smartphone is that there is a certain amount of power that can be supplied by the lightning or usb connector.
This isn’t enough to make the HD-650 shine. Look at the “portable” DAC page on headphones.com for example:
Portable DAC/Amps – Headphones.com
Many of the larger ones have a battery supply of their own. The Earmen, The iFi Hip Dac 3, many in that class will do a MUCH better job with your Senns. The specs on the Chord Mojo show you output at both 32 ohms and 300, for example.
Note if you want the additional power of balanced (and the HD-650 sounds good with balanced) you will ALSO need a different headphone cable for the headphones that uses a balanced connection.
So while a dongle type DAC/AMP will power most IEMs and easier to drive headphones, the HD-650 can really benefit from something a bit larger that can either be plugged in or has it’s own power source, not the USB connector.
I power my HD-6xx from a desktop stack, not portable - I’ve stopped trying although it sounds pretty good with the Dragonfly Cobalt or the L&P W4. There is clearly a difference when powered by my Lyr 3, FiiO K9 PRO ESS, or best of all by my Eufonika tube amp.