It sometimes comes down to the athlete and the setting. For example, Nathan Adrian was thrilled with his bronze in the 50 free. Allyson Felix was obviously heart-broken to finish the 400 meters with a silver. If the specific athlete has a lot of national pressure as well as self-imposed pressure and is favored to win, nothing other than gold is worth celebrating.
Bronze medal winners are consistently happier than silver medal winners, due to the fact that silver medal winners are closer to the gold medal they went to the Olympics to win, but bronze medal winners are just happy they won anything. I imagine it like a class- if you're top of the class, you're happy, second to the top, you're always competing, but third from the top, it's smooth cruising.
Many countries pay their Olympic athletes when they win medals. The countries that do pay, pay athletes more for gold and silver medals than they do for the bronze. The silver medalists are disappointed to not win gold and many bronze medalists are just happy to win a medal, but most people view silver as one step ahead of and better than bronze.
Each Olympics medal win is unique. Some athletes are disappointed to win a bronze or a silver medal because they think they should have won gold. Other athletes are thrilled to win any medal at all. In the end, all athletes are happy to win any type of medal, though they may wish they won a higher one.