Many questions about the difference between vinyl records and cd can be answered definitively, but if you are searching for evidence that one sounds better than the other, then you may be very disappointed.
However, looking concisely at how each option works is a good starting point.
Vinyl may be easier, since its signal is equivalent across the entire chain. All recording material is basically stored on the disc, meaning it is the only completely lossless audio format and the way it is translated depends on the turntable and other components.
Digital, CDs do not use a continuous analogue wave, they simply take pictures at various points along the wave and translate their form in 0s and 1s. A Digital to Analog (DAC) converter is then needed to fill in the missing information between these snapshots and connect dot to dot again to form an analogue wave which the speakers will reproduce.
How your configuration affect using vinyl records versus cd
Budget and good device matching obviously affect how both your CDs and vinyl sound, but with the latter it is maybe even more critical that things matter.
Set a swap correctly to start – set the right tracking weight, make sure it is level, has the right cartridge – and it is vital that there is proper help. You do not have to spend thousands on a hi-fi rack, but particularly suspended floors will emphasize the footfall and vibration of your speakers and have more output impact than with a CD player.
Whether vinyl or CD sounds better will have to do with your setup, the consistency of your personal preference and source, but in this age of ever enhanced streaming services and high-speed downloads both room and demand remain.