Everyone has commented very well on the differences. I will just add a bit.
LP's have better freq response.
Lp's have their own distortions, but the sampling of the digital process chops up the music and creates their own distortion.
LP's are like CD's, some good, some bad.
Digital is not always bad. CD and digital are a GREAT format. But it is the mastering and creating of the cd that butchers the sound.
I have good digital Telarc classical LP's and Telarc classical CD's of the exact same performances. I can create, with my own system, a much better sounding CD than the prerecorded CD. This is with a little Pioneer CD recorder deck! So CD is a good medium, but it is the implementation of the recordings on CD that is terrible.
As soon as the mixing starts, the sound goes downhill. Even with analog.
And there is the reproduction equipment. Many variables.
But a cruddy cd will sound cruddy on any system. So will a cruddy lp.
And the reality is, vinyl is available, but can be expensive or a gamble to buy. I have bought hundreds of albums on ebay. Most good. A few lemons. But at $3 a record, that's better than $17 a classical cd! LP's and their reproduction systems take a lot of work to maintain. CD's don't.
I like them all.
They all have their place, as hobbies. Don't just think LP will make great sound. It takes work.