I have a very inexpensive smartphone with a lame dac. Even my last smartphone, which was fairly middle of the road, had difficulty giving the full potential of my v-moda lp² set; while on the desktop they sounded far better with a very mediocre onboard dac.
Note that dac doesn't have anything to do with it, dac is very cheap and simple thing that only has one task, to convert digital to analog signal. People seem to give too much importance to it, but truth is that pretty much almost all nowadays dacs are sufficient and good. Most of them don't make any audible noise and all of them are sufficient to get highest dnr that your music have. There are some exceptions that are found in the worst cheap products but it's really a big nonsense for people to praise dac as some wonder so much.
Problem with driving something is amplifier, that is the thing that is responsible for noise, distortions, not being able to drive certain headphones, not matching impedance, not having enough power for low sensitivity headphones. So it's amplifier inside that is problem, dac doesn't matter almost at all (as long as it is not complete crap, which it isn't in most of today's stuff that have D/A)
24 bit music is complete hoax without it being a matter of opinion. I will tell you exact differences so you know what they are, but you can check that anywhere, just type 24 bit myth and you will see undisputable proof. Note that 16 bit audio wasn't chosen randomly by some moron, it's very precise calculation of what will be reproduced and what we can hear.
24 bit audio with higher sampling rates have technically higher dynamic range (dynamic range (DR or DNR) is range between lowest and loudest signal) and 24 bit audio has 144 dB of DNR, while 16 bit audio has 96 dB. Why this doesn't matter at all? There is no music that is recorded with more than what's 16 bit audio capable. Signal must not be too silent or it would be masked with background noise and it must not be too loud because of clipping distortions and loudness in case physical gear can reproduce it, so either way there is
no music that exist that uses that much DNR anyways. 24 bit audio also has (well possibly, that may depend) lower noise, which is
inaudible with 16/48 audio for example. And about it being able to reproduce higher frequencies (thanks to higher sampling rate) there are no instruments that use those high frequencies, and it's usually some hiss or nothing, roll off is so high above certain freq that it is as well pointless, even if there was music that uses for some reason sounds over 20 KHz, but
there isn't.
Anyways 24 bit is simply a myth and nonsense, based on placebo. It is however very useful in studio because of more headroom, but for playback and listening, it has no advantages at all. None of this is a matter of opinion, and you can check realhomerecordings channel on youtube for example to see further tests and explanations.
If built in amp in your current sources isn't enough and you are not happy than player will most likely help, tho be sure to check a bit whether you should go for lot more powerful X3 than X1, since X1 doesn't exactly have the most powerful amplifier as well. Don't worry about dac at all, it's all big nonsense and biased people spread things that are simply not true. It does matter to certain point and there are bad dacs but X1, X3 or anything else pretty much doesn't matter at all dac wise, only amplifier. To actually hear the difference from dac you would need exceptionally sick setup with perfect dead silent amp and even then it would be hard to tell the difference between two good dacs.
Also note that if you get X3 you can use it as USB dac for your desktop as well (especially because you said you are not happy with desktop sound as well), so by getting X3 over X1 you'd gain two functionalities and more powerful amp.