In one important respect, civil and criminal cases differ in the required level of proof. That is civil claims need to be proved by a "preponderance of evidence," while criminal charges need to be proved "beyond a reasonable doubt."
But my question relates to "evidence." That is, does "admissible evidence" have to be of the same or different standard in a civil versus criminal case? If "different," what would be the differences between the two cases?
Focusing on the part of the question where you say
But my question relates to "evidence." That is, does "admissible evidence" have to be of the same or different standard in a civil versus criminal case
there can be (are) some differences in admissibility between civil and criminal cases. Looking at the Federal Rules of Evidence, FRE 412, one cannot introduce "evidence offered to prove that a victim engaged in other sexual behavior; or evidence offered to prove a victim’s sexual predisposition", but distinct criminal vs. civil exceptions exist. For criminal cases,
The court may admit the following evidence in a criminal case:
(A) evidence of specific instances of a victim’s sexual behavior, if offered to prove that someone other than the defendant was the source of semen, injury, or other physical evidence;
(B) evidence of specific instances of a victim’s sexual behavior with respect to the person accused of the sexual misconduct, if offered by the defendant to prove consent or if offered by the prosecutor; and
(C) evidence whose exclusion would violate the defendant’s constitutional rights.
but in civil cases,
In a civil case, the court may admit evidence offered to prove a victim’s sexual behavior or sexual predisposition if its probative value substantially outweighs the danger of harm to any victim and of unfair prejudice to any party. The court may admit evidence of a victim’s reputation only if the victim has placed it in controversy.
Also, under FRE 601,
Every person is competent to be a witness unless these rules provide otherwise. But in a civil case, state law governs the witness’s competency regarding a claim or defense for which state law supplies the rule of decision.
which introduces an asymmetry between the two kinds of cases.
There are also standards of admissibility that only apply to criminal cases and not civil ones (FRE 413, FRE 414) or only in civil cases (FRE 415)
The rules is evidence are virtually identical in civil and criminal cases. Like most state rules, the Federal Rules of Evidence begin with a rule (Rule 101) saying that they apply in criminal and civil cases alike.
There are some differences, mostly where the courts or legislatures have concluded that certain types of evidence should be treated a certain way, but where the Sixth Amendment imposes limits on what kind of evidence can be admitted for excluded.
For instance, there is an apparent conflict between the Confrontation Clause, which gives a criminal defendant the right to confront his accuser, and the rules that admit certain types of hearsay, which allow testimony into evidence without the speaker showing up to testify. In cases like these, you'll often see the Federal Rules of Evidence simply carve out a special exception for criminal cases.
Another example is Rule 404, which governs the admission of "character" evidence. There are concerns that this type of evidence is more prejudicial than probative and it is therefore generally excluded. But there are also countervailing concerns that a criminal defendant facing a loss of freedom or life should nonetheless be able to provide evidence, for instance, that he has never hurt a fly and thereforec would never have killed his wife. So again, in that case, the rule specifically carves out room for a criminal defendant to introduce that evidence, and then gives a prosecutor the opportunity to rebut that argument with evidence that the defendant has actually killed his three previous wives or whatever.
