Technically the records have a better sampling rate and have more information.
Phonograph records have no sampling rate, they are analog.
When I was studying electrical engineering, the formula given calls for a sampling rate that is slightly more than twice the highest sine wave signal you want to transmit.
Analog audio signals, no matter complex they appear, are made up of the sum of a series of sine waves up to the upper limit of human hearing. To digitize a sine wave you measure the upper top of the wave, and how low it goes under the zero crossover point. So therefore you are doing this twice for every sine wave.
Square waves are the sum of the odd harmonics of the fundamental frequency...triangular waves are made up of odd harmonics too, but the amplitude of the harmonics drop off with each increasing order...A saw-tooth wave is made up of odd and even harmonics.
The upshot is that the squiggly line that is sound is made up of various sine waves summed together, and to digitize it you have to sample twice as many times as the highest sine wave frequency in the signal.
CD's were designed to transmit a frequency range of 20 Hertz to 20,000 hertz. So they chose a sampling rate of 44.1 Kilohertz...a little more than twice the highest frequency.
As a comparison FM radio was designed with a very sharp 15 Khz cutoff. That is, it does not transmit anything higher than 15 Khz.
Cassettes "rolled off" generally above 10 Khz...With the high end chrome cassettes they could be made to record up to 15 Khz in high end machines. (Those "featured midnight albums" of hard rocks stations in the 1970's.)
LPs were generally rolled off above 20 Khz...