They are quite similar and are often used interchangeably. However, they do not have exactly the same meaning, so in some cases you would use one instead of the other.
Conclusive relates to a conclusion, so is basically about finding the answer to something. Decisive is more about making a decision, so if it is decisively proven the answer has been decided, rather than concluded. Talking about evidence in court you would usually say it is conclusive, so it shows the answer for whether someone is guilty or not.
Sometimes it doesn't matter, but in science or law you want the facts to conclude something rather than be decided.
The victory was decisive.
She thinks quickly and is decisive.
The study conclusively showed the medicine worked as a cure.
The evidence conclusively showed he was innocent.
The jury decisively replied, "Not guilty".