I don't know what powers the loudspeakers (probably the qualcomm chip), but the headphones are powered by the two TFA9890. Together, they are able to not only decipher files up to 24 bit FLACs (proper High Res, aka above CD quality, unlike most smart devices which will only playback 16 bit FLAC files, aka CD quality), but with no hicups, clear separated sound, and frequencies from 3hz up to 96khz, which is amazing. I don't want to get in the debate of our human hearing, which is much less than that, but the point is because of it's wide frequency range, the "steps" between each frequency are much denser (if shown on a graph), which translates into clear sound, with distinct sounds that don't overrun each other, and more importantly superb sub bass, which is rare. All this, of course, provided you have some very good headphones, like the superb MDR 1A which I can confirm sounds amazing, significantly better than the old MDR 1R, but also with select Sennheiser, AKG, and other brands specialized in headphones. If you use it with Beats or the like, the effect of the TFA9890 dac/amp chip won't be significantly different than playing it on other devices, like the new iPhones, which unfortunately are not able to decode high res audio.
What the Z3 also has that no other phone has, is DSEE HX. This is a technolgy which upscales lower res, even mp3 files, to near high res, by intelligently filling up missing frequencies (similar to wha the X reality engine does on 4k sony TVs, which is the best full HD - 4k up-scaling technology). Many say this is a gimmick and they can't "see" how it can make a difference. Anyone who says that, obviously never tired it out, either on the Z3 or other Sony audio components. When listening even to 320 kbs Mp3, the difference in clarity, detail and soundstage is HUGE between setting it on and off. I suspect the TFA9890 (actually i'm fairly sure) helps out a lot in this process. The difference can not only be clearly heard, especially on high res headphones, but it does seem to affect the battery a bit as well, speeding up the battery drainage while listening to music with the setting on by about 10%. This is a clear indicator that there is some pretty intense hardware working (probably the CPU + DAC) to fill up those frequencies.
In short, I can tall you this, out of my experience:
Before my current setup, I had a z1 (non high res, standard Qualcomm DAC doing all the work) + MDR 1R. It sounded good, of course, but I eventually got a Fiio e11k in order to bump up the volume and lacking bass. Now, that I got the Z3 and the new MDR 1As the differences are as follows:
-The Z3 even with the MDR 1R sounds SIGNIFICANTLY clearer and better in every aspect (with the same audio files) than on the Z1. This clearly has to do with the new DAC inside. Lower quality FLAC and MP3 files, when setting the DSEE HX on, also sound like they're properly better quality files, with much MUCH more detail.
-The Z3 + MDR 1R sounds better even in the bass department, and there's a volume bump of about 10-15% over what the Z1 could deliver with this setup
-The Z3 + MDR 1R + Fiio E11k is no longer viable. While the Fiio amp helped with the Z1, with the new chips inside the Z3, it actually kind of destroys the sound, making it sound louder (obviously, being an amp) but much more muddier and less crisp.
-The Z3 + MDR 1A seems like the perfect portable audio combination on the market (excluding high end audio players, i'm talking about any smartphone + ipods). The overall sound and especially the bass on the MDR 1A sounds better than the MDR 1R. It also sounds quite a bit louder, being a lower impedance headset (24 ohm vs 48 ohm for the 1R). The Fiio E11k is already up for sale as it's become useless.
Basicallly, yes, the Z3 is without a doubt the best smartphone on the market for audio playback. I have tested it DIRECTLY with an iPhone 6 plus, and the difference is quite significant. But being basically a high end, high res audio player, you can only see it's true color with really good headphones. So if you're into audio, and chances are even if you're not and are going to buy a Z3, you will get into good quality audio, you MUST invest about 300$ on a good set of headphones. Besides the MDR 1A, I would recomend some AKG K550, JBL Synchros S700, JVC HA SZ2000, Sennheiser HD7 DJ, Audio Technica ES700, Sony MDR-1R, among others. If you have upwards of 1000$ to spend, the only headset recommended for mobile devices at that price range would be the Denon AH D7100 (i believe it's more than 1000$ actually, maybe 1300$). Those are all over the ear headsets. There are quite a few in ear high res headphones from the same companies as well, but I'm not that much into them, so I don't know what to recommend (I only use in ear at the gym, the Sony MH1c which were privided with my Z1, very good 70 dollar headphones, but in no way high end).
On last thing, regarding volume. As I said in a previous post, ALL sony portable devices (xperias included) are set with pretty restrictive volume limitations. That's why if you compare a Sony Xperia Z3 volume output with an iPhone's, for example, it will sound quieter. So what you hear out of your Z3 when setting it at the max volume, is actually about 60-70% of what the internal amp is capable of. Now, with some headsets that's no issue. With the MDR 1As, when set at the max, it right at the maximum limit of what I would be comfortable with when listening no more than an hour, however with others, like the MDR 1R or AKG K550 (which I tested), the volume is lacking at the max setting, due mostly to higher impedance. The only way to get rid of this limit is by rooting the phone. I've tested this method on both the Z1 and Z3 (though I de-rooted the Z3 and am waiting for a rooting method that doesn't unlock my bootloader, if you're into that kind of thing, you'd understand), and when editing a specific file (which I will get into detail only per request), the volume boost is properly significant, on the Z3 making it sound quite louder than even the iPhone 6 plus, which probably has the highest standard max volume setting.
