The answer to this question depends entirely on what perspective you take. What exactly is meant by "better"? As MaestroECMcCloud stated, Mozart was a child prodigy and arguably among the most naturally gifted musicians of all time. He was renowned for his ability to hear things in his head and compose brilliant works almost "off the cuff." In this regard, I expect he had Beethoven beat.
That said, Beethoven's music was arguably more innovative than that of Mozart. Like Bach, Mozart was an absolute master of his genre and stretched it out to places no one else could manage. Beethoven's music, however, particularly towards the end of his life, became something entirely new that influenced generations of composers to follow him--even through today. Where Mozart's music was about the amazing agility and wit of his reason, Beethoven's music was about the depth and power of his passion. Few have equaled him in this.
From a personal perspective, I like them both, but I will always land in favor of Beethoven. I love the dark and brooding...this was his bread and butter.
Thanks for the question!