I believe the (yes lossy) HD formats has been confirmed to sound better than old SBC? standard. I dont know if there is audiably difference between "HD" and non-lossy HD. Aptx HD is already more than 4 years old. LDAC and a newer one are licence-free as far as I remember. Not sureany codecs are about the particular BT module in use +/-$2, unfortunately, all of these codecs are lossy-compressed, and "HD" just a nickname without connection to reality.
respice finem was 100% right, the most challenging thing is a high power density design with minimal EMI disturbances from SMPS to class D and to the frontend etc. One BT module to another one I think can change my 8 years old son
Cheers!