If you have won the competition in your dream, but havent achieved the first place, you will be successful in your waking life, but only at some point. Perhaps the dream suggests you to work even harder and you will be able to achieve more than you think you could.
Dream dictionary: Place(win other place, but not first) dream meanings
If you dream of taking the part at some kind of competition and winning the second place, it means that you are doing great in your life and going on the right direction, but only if you feel happy about it. If you do not feel good about it, you have to relax, do whatever you do and enjoy your life. You do not need to be first one in all aspects of your life. Perhaps you are the person who tends to win among the others, therefore you feel sad about it. The second place is the good winning point.