Saying that something sounds identical to your integrated audio doesn't necessarily make it a bad device or warrant a poor review. It would however warrant one if it sounded bad. Integrated audio and upper end smartphones measure pretty damn well anyway; and issues that passing through a headphone amp won't cover tend to present themselves quite blatantly, in the form of hiss and EMI (like my cheapo chromebook).
 
For instance your phone's measurements, which are at the bottom of the page here, are quite excellent
 
If you're already coming from an excellent source, a night and day difference (if any) wouldn't make sense. Hence it's unfair to the manufacturer to give a negative review unless they have made the claim of a substantial improvement to the perceived quality compared to these sources (beyond making them louder, which would affect that). If they are making this claim, then I will of course retract my comment.

It's a portable DAC packaged as a separate device that you would have to carry around with you in addition to your phone or tablet or other non-audiophile source - that by itself is an implicit claim that it can do something extra for you that the average phone or tablet can't. I find that it mostly fails at that (as a DAC). The Redmi 3 isn't even among the best smartphones for audio quality (just look at the comparative table - it's not being compared to any major-brand flagships, and for good reason), it's rather what you might call a "typical" smartphone for 2016 in terms of audio performance. Well, that's the reference level that a separate portable DAC has to surpass in order to be a worthwhile product. The Fiio Q1 does not surpass this level, therefore it fails in its primary mission as a separate portable DAC. (Maybe it's good as an amp, but then you could save some money and just buy an amp that doesn't claim to be anything more than an amp and doesn't have anything else priced in.)

You are partly right and justified in your rating. SInce the term "Better than your laptop/smartphone audio" or "The onboard audio is crap" has been sold blatantly and appropriate to say 'abused'. It has become a marketing term. However the consumer should use a little discretion of his own when buying a product. 
 
Though, I had a similar experience as yours. I had heard so many good reviews of Fiio E11 amp and when I finally bought it couldn't bear the bloaty muddy sound. Sold it the second day.

In my experience, differences among DACs and Amps are recording dependent and headphone dependent. I've enjoyed the Q1 with both Beyerdynamic DT880 and Sennheiser HD650, it was clean and powerful enough to my ears. In audio, a chain is no stronger than its weakest link, if the headphone happens to be the weakest link in your chain then you won't get the benefits of a quality DAC/Amp. That said, differences among DACs and Amps are subtle in the big scheme of things, and most of the times you'll need high quality recordings to expose them. This remain true even if you decide to spend 10 times more than the price of a FiiO Q1.

I don't think that there is anything inherently wrong with the Q1 and would echo the other comments in that the difference you hear when connected to your source will depend on how good or bad the quality is direct from that source. I have a very cheap Windows tablet and a cheap Chromebook, the sound quality direct from both of these is truly awful, connect the Q1 and there is a very clear and noticeable improvent, the same isn't true when I connect it to my Samsung Galaxy S7E, although the Q1 gives me more power.
 
My own view is that the Q1 is a decent entry level DAC/AMP and can be an improvement over a devices built-in sound. When price is taken into account it represents reasonable value for money but if looking for a portable USB DAC around the same price point I would go for the AQ DFB (in fact I did).
 
Also keep in mind doing that when using an external DAC with Android do your testing using UAPP as it seems to provide a better overall output than Android apps that send audio through the Android system. I have found that the exact same track played through the stock Apps will sound different and better when played through UAPP. Android doesn't really seem to play nice with USB DACs.

@Me x3
I know this can be a problem, but at the same time you have to take into account that the people most likely to buy an entry-level/affordable DAC are also likely to buy entry-level/affordable headphones. If this DAC only works properly with god-tier headphones, that could be seen as another failing or another way of saying it doesn't provide much benefit by itself.
 
The source files I played were all either 320-kbps MP3s or VBR AACs around a 300-kbps average (Q 0.8).
 
@west0ne 
If the Q1 provides an improvement over some mass market devices and not over others, it will get good reviews from owners of the former and bad reviews from owners of the latter. Such is life.

And I did use UAPP for playback.

I understand your perspective, but there's no device able to improve the sound of the headphone. The chain is no stronger than its weakest link. One link can not make the other link stronger. DAC/Amps should make the headphones sound as good as they can. That's the DAC/Amp's purpose. The fact that FiiO Q1 is affordable has little to do with the pairing, it works very well with quality headphones and that's a lot to say for such an affordable and versatile device.
 
Sometimes the problem lies in budget allocation, the headphone is the most important link, so it's wise to spend more on the headphones and then start thinking about the DAC/Amp.
As an example, the Sennheiser HD650 + FiiO Q1 sounds better than the Sennheiser HD558 + Schiit Bifrost4490/Asgard2 (which is a much more expensive combo based on a lower grade headphone), you get the idea.
 
Last but not least, with quality recordings I mean those from audiophile labels such as Chesky Records, 2L, LINN, etc. Recording quality is much more important than file quality.
A poor recording, over compressed/edited at the studio, won't sound good no matter how transparent your rig happens to be. You can have 24/96 Flac files that sounds like rubbish.
On the other hand, a high quality recording of a live venue, made using minimalistic techniques in order to preserve the tonal balance and soundstage clues is much more likely to shine when played on a quality setup, even if it was properly encoded as a 320kbps lossy file.