I bet you couldn't tell the difference in a Bluetooth blind listening test. Also, how could AAC over Bluetooth sound better than wired? Where is the evidence? I think people go overboard in placing importance on codecs for Bluetooth. If the source files are of sufficiently high quality (ie at least hi bit rate lossy), then differences between codecs are inaudible.
256kbp/s AAC files are either passed through directly to the headphone or transmitted at 264kbp/s on an iPhone to ensure no quality loss. Due to the wireless nature, the headphones are utilizing their own amp and DAC rather than relying on the source device. Assuming proper design and a quality amp/DAC, this leads to a better sound than an unamp’d wired connection as there is no degradation in file quality and the headphones are utilizing components designed to make them sound their best.
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