Analog can sound a lot worse than digital... but also a lot better.
Analog has an advantage due to the type of materials you are working with. Records' only sound limits (audible to the ear) are those that you put on them. In other words, a fresh, clean, hardly-played vinyl on very good equipment will sound fantastic -- better beyond your wildest dreams ... certainly not something your CD player could do. However, take that same vinyl, play it a lot on an old stylus and without ever cleaning it -- and you'll get sound much worse than digital. The only real limit the listener has is that of the limits of the physical media. And, of course, vinyl junkies who are dedicated enough (and there are plenty, including I, here, if you have more questions) will be able to experience some of the most rewarding and pleasant sound to ever come from recorded music.
But this is also assuming that the actual recording is good too.
Remember that if the LP of 'Kind of Blue' has bad EQ bends and a bright sound to it, and the CD doesn't, that the CD will probably sound better most of the time. However, because this is not the case, the LP version has the ability to sound a LOT better.
Basically, vinyl is a whole other hobby in itself. It takes cleaning, care, and collecting. It also takes money. You will need to spend quite a bit of money on accessories including a record cleaning machine, brushes, fluid, and other things to get the most out of both your vinyl and your turntable. But in the end, it's very rewarding.