I've been buying Vinyl records for three years now I think, and I absolutely love it. Make no mistake though, Vinyl is not perfect, and it is a major pain in the ass at times but the moments were it all seems to align and even that horrible beat up record comes to life it can be an amazing experience. The question of whether Vinyl sounds better than a CD is a long answer, if both existed in a vacuum, and the music contained on both discs were recorded by the same method, and played on similar quality equipment, I believe that Vinyl sounds better than a CD. In the real world? Maybe. If you listen to a lot of old rock like Pink Floyd or Led Zeppelin, where music was recorded on analog equipment, and mastered with care Vinyl really shows its strength. Part of that though is because some remasters (sadly the Led Zeppelin remasters have fallen victim to this) are mastered with loudness in mind. The sound difference between Led Zeppelin IV on worn 40 year old record sounds much better than the recent remaster, and infinitely better than tracks from the album Mothership. With more modern albums some of the Vinyl's are cut from the CD version of album, so while the loudness war doesn't exist on the Vinyl in the same way as it does the CD, and the dynamics will be slightly better, the Vinyl wasn't remastered and most of the dynamic compression still exists, and at that point the price difference and sound quality between the two really isn't worth it unless you love the format like myself.
I do think Vinyl is something you should experience in your life however, eventually I will have to switch over to digital music. Vinyls are not going to last forever, or sound great forever for that matter, and eventually they will likely no longer be produced because lets be honest if music starts being recorded and available for download in Lossless 96000Hz/24-bit or higher quality, there really would be no point to buying a physical format anymore.