mp3's are compressed, and no question at all quality can suffer greatly there depending on how much compression is requested. The MP3s played by many radio station for instance, are total trash (those on streaming sevices vary). But a CD, which is the correct comparison to an LP, is not MP3s, it's made of .wav files, which is not a compressed format. In a wav file the input audio stream is digitized 44,100 times per second and 65536 (16 bits) possible volume levels on each channel. There is no loss detectable by human hearing (which tops out at about 15,000 Hz), and just as importantly, no recording device with more than 16 bits of dynamic range for making a recording. There is something missing in digital recordings, it's that little bit of white noise from the master tapes (from old stuff) and the 'grey' noise from the vinyl surface. That can 'soften' the sound of recordings make in too live an environment and make it sound 'better'. But it is not a more 'faithful' reproduction - you're mostly exposing poor production choices.
It's sort of the same effect as the need to soften the focus on high res cameras when shooting close-ups in film. It can be disconcerting to see a face in that kind of detail across a 30 ft screen. But don't blame the camera.