i've always felt that the wired connection is better than bluetooth, tho the difference is much less with the newest bluetooth aptx codecs (provided your devices support them)
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Wired is better. However, do not rely on the inbuilt DAC of most phones (Iphones are OK but most others not). As long as you are not hoping for the very best, but only for a big improvement with most phones, get a Behringer UCA 202 external usb DAC in between the phone and the amplifier for much much better sound (if you can get a usb signal out of your phone).
See here for more detail on Bluetooth quality: http://archimago.blogspot.nl/2017/12/measurements-oppo-sonica-dac-and.html
It will depend case by case. DAC used is the biggest factor. Newer Bluetooth technology can be quite good. Traditionally, wired has greater upside. Try both and see.
Using a good outboard dac with wired connection is probably the surest bet for best sound. I’ve gone that way with a Chord Mojo DAC. Not only is it great with headphones but as an input to a good hifi as well. I went for bust and connect it to line level inputs using a very high quality Mogami gold mini stereo to dual RCA Y adapter. The results are absolute top notch.
Bluetooth was a replacement for infra-red controllers. (There was actually a better solution at the IEEE but BT won because of the companies that came up with it) Bluetooth is to USB is to Ethernet. Folks don't run data centers on Bluetooth and USB.
The Cirrus chip that powers your headphones, at least in an iPhone 6 and 6S, has lower noise and distortion than the digital interface even if you plug "colorful bugs" into it.. Plus, these "bugs" do not bypass the 44.1K limit Apple for one has placed on their devices although now they can unfold Stuart's latest marvel I am told. Sneaky.
However, you can load and download 192k/24 bit files, etc., via wifi to your phone and then play them back bypassing the dumbing down digital circuits using the $30 Apple Camera adapter. You then plug your interface(s) into it for true hi rez sound to your headphones. YMMV.
The same general thing goes for preamp input sorry that was the original question. I'd stick with the headphone jack. Belden cables are $30. Preamps have BT in them now? I do some streaming through an iPAD via the headphone jack of some services and if the recording is good at the highest quality level and fastest Arrris wifi 5 GHz the sound is acceptable for casual listening.
A friend of mine was at Munich and told me some fellow this great sound in his STOA system off his iPhone sans "bugs or Bluetooth". I explained the various ways it was done.