No, I don’t believe civil and criminal cases should be proven in the same manner, but should have different burdens of proof. This is because the courts are dealing with two different objectives. In a criminal case the objective is punishment and looking after the public interest. The objective of a civil case is a redress of wrongs and addresses a private matter between two parties. In the United States, criminal law is considered more serious than in civil law, which can be seen in the fact that criminal defendants have more rights and protections than civil defendants. Because of this, as mentioned in the previous post, punishment for each case is different.
I assume that you are talking about standards of proof in the two kinds of cases. In the US, a prosecutor must prove the defendant's guilt beyond a reasonable doubt (in a criminal case). By contrast, a plaintiff must only prove that there is "clear and convincing evidence" that the defendant in an important civil case is culpable. I think that it is important to have differences between the two kinds of cases.
The reason I think this is that criminal cases are clearly more important than civil cases. In a criminal case, the defendant can go to prison or even be executed. This ought to have a higher standard of proof than would be required if all that was at stake was money. It is not to say that money is unimportant, but it surely is less important than being sent to prison.
So, I think there should be different standards of proof since criminal cases have so much more impact on the lives of the defendants.