Let's say we have one good boom mic and several recording devices. For instance boom mic plugged into zoom h1n, zoom h2n, zoom h4n, smartphone, dslr etc. What technical features of those recording devices determine the quality of the sounds.
Obviously the preamps and the A/D converters. Some say, devices differ in terms of phantom power, but I don't know about that. Also be aware that of the mentioned recorders only the H4n has XLR inputs. For the other ones you would need adapters and/or an additional mixer. In using a mixer e.g. a Sound Devices MixPre in the signal chain, you would have good preamps but a comparability between the recorders would be useless.
There are several variables here. First of all, the preamps can have a lot of impact. Bad preamps may result in more noise, distorted sound, etc. The phantom power can also affect the sound; not enough current or power can affect the performance of the microphone. The AD converter inside the device can also affect the sound, although how much of this is noticeable I wouldn't know.
Once digitized the sound shouldn't be affected, but as you mention using a smartphone; what format does it save the file as? Mine has an option of saving a recording as uncompressed PCM, but by default it encodes to Mp3. Depending on the bitrate, this can also affect the sound you hear afterwards.