They use the exact same DAC/amp chips and are entirely identical in terms of sound quality and output power. The Qudelix has slightly higher max voltage output than the BTR5 for high impedance cans (this is presumably just a software limit on the latter as they are literally the same chips) but they have the same power into the lower impedances of Hifiman planars and will be exactly the same.
The Qudelix is smaller, lighter, integrated clip and has a much better app and PEQ support. BTR5 has the screen showing volume and input which is nice, and better buttons. Q5K has much better battery management, BTR5 is always charging while Q5K can actually run off USB power. So BTR5 if you use it plugged in a lot the battery will degrade after a year or so while Q5K is fine. I have both around 2 years, and this was my experience.
Qudelix IMO is the much better all round device.
"HiFiMan planar magnetic cans" isn't very descriptive as Hifiman make some of the easiest to drive headphones (OG Ananda- 103dB/mW) and some of the hardest (HE6SEV2- 83dB/mW). MOST Hifimans can be driven satisfactorily from either Q5K or BTR5 using a balanced cable though, I have tried HE1000 Stealth, Arya Stealth, OG Ananda, Sundara, Edition XS, HE400SE. Edition XS and HE400SE are the most marginal but still OK. All the others I think absolutely fine. I have even tried the HE6SEV2 and it actually makes noise but wouldn't be a rec.
There are some similar devices, made just for car use mind you unlike this one, for sale on Amazon with the exact same specs as this unit that plug in to your car's USB power connector and then have a cable you plug in to the AUX auxiliary input. One even uses the LDAC Bluetooth codex - the closest to lossless Bluetooth codex available. It costs a fraction of this device around $25 and sounds great. It turns on and off automatically by simply turning your car key (even just to the point where you get power to the car but has not cranked yet - hope that makes sense) - as well as connects automatically - zero interaction needed. If your interested I can get the name of the device for you though it is easy to find with thousands of high reviews and the only LDAC codex one available.
This isn't for bluetooth headphones. It is a bluetooth receiver so you can send audio via bluetooth to wired headphones. It doesn't accept other wired peripherals. It is strictly for wired headphones.