Just to be specific about the ways that a digital format might compromise the original audio, there are two separate phenomenons. One is quantization (which is how many bits the recording is at -- e.g. 16, 24, 36, etc.) and determines how many possible numbers are used at any time to represent the amplitude of the waveform. The other is sampling, or discretization, which represents how many snapshots of the waveform occur in the time domain. This is the sampling rate -- e.g. 22khz, 44.1khz, etc.
Discretization results in the limiting of frequencies that can be represented in the digital file. Specifically, the highest frequency that can be represented is half of the sampling rate. So at 44.1khz (which is the sample rate for all CDs), the highest frequency that will be present in the recording will be 22050hz. Higher frequencies have to be filtered out of the recording before being sampled because otherwise a phenomenon called aliasing will cause higher frequencies to instead become much lower frequencies. This is similar to when you're watching a car ad on TV and the wheels appear to be moving slowly backwards instead of quickly forward, due to the TV's refresh rate. Note that the upper range of human hearing is about 20khz, although it is said that even higher frequencies that you can't hear make some sort of perceptual difference in the vinyl playback.
Quantization error results in an annoying type of noise that depends on the amplitude (loudness) of the sound wave -- it is a weird sounding distortion that doesn't occur when silence is in the digital file (it's totally quiet at that point) but is loud and annoying when at a higher loudness. Unless you manipulate something to a very low bit rate, you generally won't hear this. However, the effect of this noise might be a cause of the "worn out" feeling some people report when listening to CDs for a long time. A common practice is actually to add white noise to a recording which will increase the noise floor so that the quantization noise falls under that level and is masked. This is called "dithering".
Modern digital recording is frequently done at 96khz and 32 bits. This means the highest frequency that can be represented is 48khz, well above the human hearing range (dogs can hear higher frequences though). 32 bits is a very detailed representation of the amplitude of the waveform. So I don't think the technology, if used correctly, inherently makes new vinyl sound worse.
There are other issues affecting new vinyl reissues -- e.g. the source of the master (e.g. tape or vinyl), the condition and degradation of the source, the original recording quality, processing of the audio, etc. I just wanted to make explicit the specific effects of digital recording and make the point that if used correctly it should not be responsible for any loss of quality given the current high bit and frequency rates available.