You question is akin to opening a Pandora's Box (and my response will likely trigger it). Vinyl zealots (not meant to be derogatory) can make the tea party look like tax and spend supporters, but....Technically the CD format is superior to LP. Also you are asking "more" but not defining what you mean or want to know. There is NO WAY to make a 100% true quantitative comparison (like which glass contains more liquid) between an analog and a digital recording (apple and oranges) because of the fundamental/technical differences.
Here is just a general idea of CD, DSD (SA-CD) and vinyl and the two spes (Dynamic range and frequency response) that have to most to do with the "content of the sound" they can contain.
Dynamic Range: CD-96db (16bit x 6dB, no noise shaping), DSD-120dB (1bit all noise shaping), LP-<70dB (rumble, motor noise, and other factors usually lower this)
Frequency Response: CD 1Hz-22.05kHz (flat, but an absolute cut off Nyquist filtered), DSD-1Hz-120kHz (flat, usually filtered), LP-20Hz-20kHz (+/-3dB, but can be higher/lower)
For comparison 96/24 (the current gold standard and most used recording/Mastering format)
Dynamic Range: 144dB (24x6, can use some noise shaping to increase)
Frequency Response: 1Hz- 48kHz (flat, but an absolute cut off Nyquist filtered)