When there's a conflict, who has the Burden of Proof in a legal conflict? Plaintiff (accuser) or Defendant (accused)?

If there is a plaintiff, this is a civil case and the burden of proof is "balance of probabilities". The judge has to decide who is more likely to be right and rule that way. This is not a criminal case, where the burden of proof is "beyond reasonable doubt".

Plaintiff.

Not all legal conflicts involve a plaintiff and defendant, but when there is someone bringing a criminal complaint against someone, they have the burden of proof. The plaintiff in such a case must supply evidence for their complaint sufficient to convince a jury of the defendant's guilt. Should the defendant perjure themselves on the stand during these proceedings however, that becomes a separate issue entirely.

In our legal system, there's a presumption of innocence unless facts can be shown to indicate that the defendant has done something wrong.

Always the accuser, you have to prove damages.

The plaintiff always has the initial burden of proof.