I would say interfere has a negative connotation. If someone or something is interfering, it is preventing or impeding something. For example, "my brother constantly interferes with my work" means that my brother prevents me or slows me down from getting my work done properly.
I would say intervene means you are getting involved, but with the goal of preventing something bad from happening. For example "The teacher intervened to stop the fight so no one would get hurt".
In both cases something is being hindered or prevented, but the goal is different.