[Xperia Z5 Compact General] smartphone-tester:
Just to chime in here as a happy Sony Z* compact user. For a bit of context, in my research group we have 1 Z1 Compact, 1 Z3 Compact, and 2 Z5 Compacts, which we use mostly for work with accelerometer sensing in the background. The Z1c was one of the first devices to come with a dedicated small core to process sensor data for the step detector, and you can constantly listen for steps and only wake up to sample the accelerometer at full speed when the device is in motion without a significant impact on battery life. Now there are a few other devices that can do that as well (most 2016 models, some of the 2015 range), but the Sonys were among the first - and they are small enough to comfortably carry in tight jeans pockets, which is exactly what the research of one PhD student is about (gait authentication). <end of context>

Positive on the Sony Z* compact range:

Size! It still fits my pockets and my hands, which I can't say of many other new phones.

Flagship CPU/RAM/etc. at the time of the release.

Qualcomm SoC and radio, which supports e.g. SnoopSnitch and a few other low-level tools.

NFC chipset that is capable of reading/writing Mifare classic cards (I am aware that my group is one of very few that would probably care about the NFC chipset...).

Decent support for accessing SIM cards directly with the Sony RIL (same comment here, on e.g. the Samsung Galaxy S3 we actually had to patch the Samsung RIL, on the Sonys it just works).

Battery life is generally better than average, although in my experience the Z3c is still better than the Z5c (with current firmware releases).

Every single one of them came with a MicroSD slot. None of the Nexus do, and the Samsung Galaxy S6 doesn't have one either!

Waterproof. I tested all generations (Z1c, Z3c, Z5c) with underwater pictures and videos. The Z3c got water damaged once and was repaired without any discussion (flaps were closed while underwater for about 30 minutes in the pool, water damage markers were red, but repair shop did not complain).

Call quality is generally good and stable. (Yes, I also use it to actually make phone calls...)

Cameras are generally good with decent light conditions, but grainy or with focus problems in low-light situations. Compared to the respective Samsung Galaxy devices at the time of release (we also use that series for other research reasons in parallel to the Sonys and Nexus devices), the Sony cameras typically have a more neutral color reproduction (positive if you are into photography, but the Samsung pictures look more appealing without post-processing), produce significantly more details in the pictures (23MP for the win), but tend to be slower. Samsung pictures "pop" more in terms of color, especially in low-light settings. The Samsung sharpening algorithms (each with stock cameras) also make images appear significantly nicer for low-light conditions. All that said, the Z5 range ships with one of the best cameras currently available on mobile phones (in the Android domain, I only have personal experience with the Galaxy S7 camera which is sometimes better, sometimes worse than the Z5c camera).

The fingerprint reader on the Z5c takes some getting used to (as in how to position your right-hand thumb or left-hand index finger to make it work well). After using it daily for about a month, it rarely fails for me now - but was very annoying in the first week. I have not spent time debugging to find out if it is actually learning during use (as some other implementations do) or it was a learning effect on my side. YMMV.

I like that it still comes with an FM radio. I don't get good data connectivity at every place I go to, so being able to listen to news is a plus that I use occasionally.

ANT+ support is nice if you are into sports, although I don't actively use it at the moment and can't comment on its quality.

Settings in Sony stock firmware are reasonably close to AOSP. When you switch a lot between different Android devices, then Samsung is extremely annoying by moving options around a lot - I never find what I am looking for on the Samsungs.

If you are patient enough, all phones of the Z* range could be rooted so far without losing a single bit of functionality - that is, you can backup the DRM keys before unlocking the bootloader to restore later, and restore DRM-locked functionality while it is rooted. This is in contrast to e.g. Samsung with its Knox eFuses. Sony seems to be supportive of development, including their releases of AOSP builds for the Z3(c), and I like to support companies that do.

Negative on the Sony Z* compact range:

Not much really. As said, I am a happy user.

Screen resolution is not full HD. This has never been an issue for me for a screen with this size, but it is one item people seem to mention.

As mentioned above, low-light pictures and videos are not great (still better than most of the phones in the same price range, though).

Rooting is more involved than on other phones, i.e. may take more steps to execute properly.

At the moment, I am carrying a Z5 compact and a Samsung Galaxy S7 with pretty much the same configuration (both stock ROMs, Z5c rooted with Xposed, Galaxy S7 not yet as I don't want to trip Knox at this time). I regularly try to do the same things on both devices and can therefore compare them well. Therefore, I will just finish with a list of what I like better for each of the devices (anything not listed is pretty similar or I personally don't care about the differences):

Z5c for the size. It doesn't get uncomfortable when I sit down independently of which trousers I wear. The S7 I often have to take out of my trousers to sit down properly.

Z5c for using one-handedly. This is not even a comparison: the Z5c I can (barely, but still) use in one hand, the S7 I can't.

Z5c for switching MicroSD cards without a tool and without removing the SIM card.

Z5C for pictures outdoors or in bright indoors settings. The pictures are sharper with more detail.

Z5c for everything to do with sound. Both the loudspeaker is a lot clearer and louder with stock ROMs and the microphone does better middle-of-conference table or concert music recordings than the S7.

If you are in public transport (including planes) a lot, then the Sony passive (i.e. no additional battery, controlled by a DSP in the Sony phones and tablets) noise-canceling headphones are a really big plus. I use them in all planes, trains, etc. and it makes a huge difference. The Samsung line doesn't have a comparable alternative that I am aware of.

S7 for the screen. This is the biggest advantage - resolution, colors (and yes, size) are simply better. A minor issue is that the Z5c is bad in landscape mode with polarized sunglasses (portrait is ok, and I don't have that particular problem with the S7).

S7 for pictures in low-light settings. During evening or night-time (or dark rooms) there really is a big difference - but the S7 is not representative, as far as I am aware it is simply the best camera in low light at the moment.

S7 for camera speed - although that may improve for the Z5c with the .224 firmware that I have not yet tried.

S7 for CPU speed, although I don't have any problems at all with the Z5c in practical use (just mentioning for the sake of completeness).

S7 for speed and accuracy of the fingerprint reader, which is better than the one on the Z5c.

S7 for device security. Some parts of Knox do improve system security, and Samsung seems to be better and quicker with updated firmware in the last few months.

For me, the battery life is roughly comparable on the two. I don't get two full days out of either of them with my (completely unoptimized) use as I did with the Z3c.