The big advantage comes from its packaging and everything built into the chip. It comes in a 144 pin lqfp package, which means that routing pins can be done by a couple people with real minimal amounts of training, and it can be laid out onto a two-layer board, which tends to be a lot cheaper than a four layer board which a bga package pretty much requires. It's also got a dac and adc built in which has the circuitry to directly drive headphones, so you don't need amplification circuitry to do that. Similarly, it's got integrated power regulation, so you don't need those chips either. Finally, all the info on it is available in a datasheet you don't need to jump through hoops to read [1]. It's not as fast as a chip, but because of everything it has, it's much more flexible for when you are designing something.
The Allwinner R8 is available in eLQFP176 and also has a built in audio DAC, ADC and headphone amp. Of course, it requires external memory and all the routing headaches that go along with that, but so does the i.MX233. Power management is generally done by a companion chip from X-Powers, the AXP209.
If the CHIP from Next Thing Co. is any indication of the capabilities of the R8, the built-in audio DAC and headphone amplifier are somewhat lacking in low-end frequency response (i.e. bass) compared to what one can get in a PC, smartphone, or any other consumer-level audio player. Indeed, NTC told me on an email support thread that for their upcoming product, the Dashbot, they're using a dedicated DAC to get better audio.
I'm tempted to buy one of Olimex's i.MX233 boards to find out if the audio capabilities of that chip are better. But as I said, starting any new project today with an ARMv5-based processor just seems wrong. Technology moves on, even in applications that don't require a screen. I doubt that an ARMv5-based processor could run a modern speech recognition engine, even if only to listen to a wake word for something like the Alexa Voice Service or the Dashbot.
[1] http://www.nxp.com/assets/documents/data/en/reference-manual...