There are a lot of details as to how the different codecs work, plus measurements here showing they are measurably different.
https://habr.com/en/post/456182/
How much you can hear is another question. For casual listening, like in the context of sports BT headphones, I agree, it doesn't matter. But there is certainly the possibility of a difference in a more quiet listening environment with good equipment. I don't think this is necessarily quite like whether you can hear over 20khz. You need to bear in mind here as well that most Bluetooth codecs are absolutely ancient. Apt X is actually even older than SBC, it is literally from the 1980s. So SBC and AptX are not particularly sophisticated or efficient codecs, there are much much better ones, such as AAC. BUT even a terrible codec can perform well if you throw enough bits at it, and that's what AptX does.
AptX also has the benefit of a single standardised Qualcomm implementation with a fixed bitrate, so it's a constant that is competently implemented and you know what you are getting. SBC historically has had a wide range of implementations and you don't know if your device hasn't decided to fall back to one of the very low quality SBC modes. AptX you know you're getting 352/384, or 529/576 with HD. It's certainly possible to make Bluetooth sound bad, I mean for an extreme case just connect using the Handsfree profile and you'll see quickly enough that Bluetooth can sound terrible and very obviously terrible.
SoundExpert also has the results of some listening tests that also show a difference.
http://soundexpert.org/encoders-320-kbps
Note the "SBC XQ" at the top there is a patch to standard SBC to allow it to use higher bitrates. What I think it suggests, is that (AAC possibly excepted) the bitrate matters more than the codec, that SBC can be better than even AptX HD IF SBC is patched to run at a higher bitrate. (Worth bearing in mind that they have relatively few results yet on SBC XQ / AptX, so, the results may not be reliable). You can participate in the listening tests yourself so they get more data, they give you files without telling you what they are and ask for an opinion.
The issue with doing this is, to support this special SBC, you would need to root/install a custom ROM on your Android phone, or run Linux. Standard Android, iOS, Windows and Mac won't do it. But it does look like a very good option if you CAN get it working, as it has basically universal receiver device support- almost any Bluetooth receiver made in any way recently will actually process SBC at much higher bitrates. So you can get what is possibly better than AptX HD quality, to basically- any Bluetooth headphone out there. And all the headphone needs to support is bog standard SBC.
http://soundexpert.org/articles/-/blogs/audio-quality-of-sbc-xq-bluetooth-audio-codec
They don't have LDAC in those tests. But as LDAC runs at a higher bitrate, and it does seem that that is the most important thing, it stands to reason that LDAC will probably do well. Certainly at the 990kbps setting- at that, it is above the average bitrate of 44.1/16 FLAC and very likely can pass MOST content lossless. I find LDAC 990 to be choppy on my phone but possibly a dedicated transmitter like the FiiO BTA30 would have the signal strength to run it reliably. It's really not for me, it depends too much on environmental interference. Sometimes it's fine, when I'm at home, although I do get degraded range, it will break up if I go far enough away (to another room). Other times though even sitting right beside my phone, it's very choppy. 660 is rock solid though and that's still quite a bit over AptX HD which I believe is 529 at 44.1 (the 576 is for 48 or 96).
As noted in the context of "SBC XQ" there is also LDAC support now in Linux, so if you are running Linux you should be able to transmit LDAC from that with any Bluetooth adapter, with the LDAC encoding being done in software.
https://github.com/EHfive/pulseaudio-modules-bt
Someone managed to get it working in Windows using Linux in a VM as the passthrough, and a dedicated BT transmitter. I'm planning on trying this myself, but if you are running Linux natively you should be able to get LDAC working on that using Pulse Audio.
https://www.reddit.com/r/SonyHeadphones/comments/jebd31
https://habr.com/en/post/456182/
How much you can hear is another question. For casual listening, like in the context of sports BT headphones, I agree, it doesn't matter. But there is certainly the possibility of a difference in a more quiet listening environment with good equipment. I don't think this is necessarily quite like whether you can hear over 20khz. You need to bear in mind here as well that most Bluetooth codecs are absolutely ancient. Apt X is actually even older than SBC, it is literally from the 1980s. So SBC and AptX are not particularly sophisticated or efficient codecs, there are much much better ones, such as AAC. BUT even a terrible codec can perform well if you throw enough bits at it, and that's what AptX does.
AptX also has the benefit of a single standardised Qualcomm implementation with a fixed bitrate, so it's a constant that is competently implemented and you know what you are getting. SBC historically has had a wide range of implementations and you don't know if your device hasn't decided to fall back to one of the very low quality SBC modes. AptX you know you're getting 352/384, or 529/576 with HD. It's certainly possible to make Bluetooth sound bad, I mean for an extreme case just connect using the Handsfree profile and you'll see quickly enough that Bluetooth can sound terrible and very obviously terrible.
SoundExpert also has the results of some listening tests that also show a difference.
http://soundexpert.org/encoders-320-kbps
Note the "SBC XQ" at the top there is a patch to standard SBC to allow it to use higher bitrates. What I think it suggests, is that (AAC possibly excepted) the bitrate matters more than the codec, that SBC can be better than even AptX HD IF SBC is patched to run at a higher bitrate. (Worth bearing in mind that they have relatively few results yet on SBC XQ / AptX, so, the results may not be reliable). You can participate in the listening tests yourself so they get more data, they give you files without telling you what they are and ask for an opinion.
The issue with doing this is, to support this special SBC, you would need to root/install a custom ROM on your Android phone, or run Linux. Standard Android, iOS, Windows and Mac won't do it. But it does look like a very good option if you CAN get it working, as it has basically universal receiver device support- almost any Bluetooth receiver made in any way recently will actually process SBC at much higher bitrates. So you can get what is possibly better than AptX HD quality, to basically- any Bluetooth headphone out there. And all the headphone needs to support is bog standard SBC.
http://soundexpert.org/articles/-/blogs/audio-quality-of-sbc-xq-bluetooth-audio-codec
They don't have LDAC in those tests. But as LDAC runs at a higher bitrate, and it does seem that that is the most important thing, it stands to reason that LDAC will probably do well. Certainly at the 990kbps setting- at that, it is above the average bitrate of 44.1/16 FLAC and very likely can pass MOST content lossless. I find LDAC 990 to be choppy on my phone but possibly a dedicated transmitter like the FiiO BTA30 would have the signal strength to run it reliably. It's really not for me, it depends too much on environmental interference. Sometimes it's fine, when I'm at home, although I do get degraded range, it will break up if I go far enough away (to another room). Other times though even sitting right beside my phone, it's very choppy. 660 is rock solid though and that's still quite a bit over AptX HD which I believe is 529 at 44.1 (the 576 is for 48 or 96).
As noted in the context of "SBC XQ" there is also LDAC support now in Linux, so if you are running Linux you should be able to transmit LDAC from that with any Bluetooth adapter, with the LDAC encoding being done in software.
https://github.com/EHfive/pulseaudio-modules-bt
Someone managed to get it working in Windows using Linux in a VM as the passthrough, and a dedicated BT transmitter. I'm planning on trying this myself, but if you are running Linux natively you should be able to get LDAC working on that using Pulse Audio.
https://www.reddit.com/r/SonyHeadphones/comments/jebd31