This isn't reflection of all headphones but it gives you an idea of latencies between the different codecs.
Your best bet is something with AAC even though it'll still not be ideal. You absolutely do not want SBC for gaming. Avantree's proprietary Fast Stream is 70ms and is responsive enough, but the Mobius doesn't support it. It might be connected to AptX, hence why my Portapro reads it, but the Mobius doesn't. I'll test the Creative Soundblaster Jam to see which it defaults to.
Now... LDAC is a low latency codec, and having JUST talked to Sankar of Audeze about it, he has his reasons why it was chosen over aptX.
His reasoning has convinced me, and I can't divulge, but it makes ALL the sense, particularly with the way the future is heading.
Me and some of you guys that use dongles are part of a niche, while Audeze is thinking about mass market where LDAC is only becoming bigger and bigger.
He did clarify though that AptX LL is limited to things like dongles. Mobile devices don't support it.
The only thing that is uncertain is what the latency numbers of LDAC is. In my case it's not an issue since I only use my phone for non-gaming use.
Perhaps in the future, there will be dongles that support LDAC. That is best case scenario.
He could've chosen AptX but it's a competing product to LDAC so it was one or the other, and trust me, you want LDAC.
So in our use case we are 'currently' out of luck with devices to transmit to Mobius, but the future may be quite different.