While I believe that the better vacation spot always depends on what the individual wants and needs in a great escape, my personal opinion is that the mountains are better than the beach. My life has always been in the city of Buffalo, New York. A climate that changes from every season in the span of a single month. I enjoy the warm weather when it comes; shedding some layers and going for a quick dip in the pool with the guys. My favorite time of the year, however, are the cold months. Those chilly nights where you can sit back with that special someone and get cozy with a cup of cocoa and a good movie.
The beach is all well and good for those tanning freaks who like to lay out in the sun all day and get some really nasty and/or unique tan line. You can run out to the surf and dive in to cool off in the disgusting, polluted waters, maybe even play a game of volleyball and get some second degree burns from the boiling sand. To me, going to the beach is like getting stranded in the desert. If you can't drink whats there, and you didn't bring anything with you, you're out of luck.
Also the sheer numbers of people that go to the beach and take up all the space, confining you to a five foot stretch of beach that random beach walkers invade constantly. To get any privacy, you would need to buy your own Island with the whole set up (and if you are that rich, sorry, this message doesn't pertain to you). And don't even get me started on the old/obese people who still think they look sexy in a bikini or speedo. Believe me, for the sake of more people's eyeballs, you are not sexy.
Mountains. they are comfortable, secluded areas that you can make your own. Lush greenery and fantastical views are always the perfect answer for those seeking a little R and R. The air is fresh and the rivers; clean. Enjoy every moment of the rising peaks and rolling hills of the mountains.
I prefer the mountains mainly because if I am looking to relax, I don't go to a hot, crowded area right on the edge of a loud, obnoxious city. I want a place where I can forget all my troubles in the piece and quiet of a mountain vacation spot. It's nice to get away from it all with a good book, or watch the billions of stars twinkling in the night sky.