AptX HD is capable of being switched down from 48/24 to 44.1/24, I know that much because Neutron player can target the output to AptX HD according to the source sample rate and send it compressed at 576 Kbps, I see the Bluetooth sample rate as 44.1/24 most of the time, thanks to Radsones ES100 App, I get this feedback for their device.
AAC is a great codec, much better quality algorithm than AptX, unfortunately AptX has been overhyped and is quite clearly a low efficiency codec compared to AAC because it is mostly designed for low latency and cheap hardware.
That being said, AptX HD is a different kettle of fish, it is superior to to Bluetooth AAC not because of the algorithms, but just because of 24 bit dynamic range in encoding/decoding and the data rate is 576 Kbps, which for a dynamic range that large, ensures that the quality improvement is almost linear over AptX at 352 Kbps.
That also puts it above AAC at 256Kbps 16 bit too, I couldn't hear the difference on the ES100, but honestly I think that's down to the DAC and AMP on that device being pretty good, but not good enough to reveal the details necessary to pick the difference (it's a great portable device really)
Not many people here have mentioned the chain they using to try to discern the differences between codecs. I think that would be essential since I wasn't able to hear compression artifacts until my equipment chain was able to reveal it.
The first time I heard the difference between AAC at 320Kbps fixed rate and FLAC, was when I combined a decent DAC (ESS 9018K2M in an M8 desktop DAC) with a decent desktop Amp (Xduoo TA-02 with S/N 110dB) and a very good good pair of cans (Beyerdynamic T1)
It was extremely subtle, but the differences were in the interpretation of shape of atmosphere in the source - if the source could reveal a rough room size and shape, then the compression changed that feeling noticeably for me - in recordings that were good enough.
Spatial positioning was also affected, but I wouldn't get this right every time, it was very subtle.
I'm quite happy with AptX HD, as it finally has enough data rate to mean that the only way I could possibly tell the difference between this and uncompressed would be if I spent $10,000 on equipment to reproduce an analog stage that would reveal such tiny differences, even then, I might not pick it at all.
AAC is a great codec, but allowing for an efficiency improvement of maybe up to 20% to 30% over AptX at the same data rate, AptX HD is maybe around 30% more accurate and also low latency.
What happens to MP3s over Bluetooth ? They get worse than they are of course, no matter what codec, another reason to favor a bit of headroom in lossy quality.