Yes
Who the jury believes is pretty much the heart of every case, not just those about sexual assault.
new-south-wales
The alleged victim will give evidence, and the police officer(s) to whom they reported the crime would give evidence of the complaint ("complaint evidence"). The defence will be entitled to cross-examine these witnesses. The defence may, or may not, call the defendant to give evidence - they will then be cross-examined.
There is not "no evidence either way" - That is the evidence. "Who to believe" is what the jury/judge does. The jury will decide, based on the testimony, if the Crown has met its burden of proof beyond a reasonable doubt.
That testimony will be considerably more than "what exactly was privately said" although that will be highly relevant. The testimony will likely describe in minute detail what each party said and did. It's likely that neither party's testimony will be entirely self-consistent (memory is fallible after all) and, certainly, they will directly conflict on important points. Deciding what to believe from each party's testimony is the entire point of the jury.
For the specific crime of sexual intercourse without consent (s 61I Crimes Act 1900), the Crown must prove:
that, at the time and place alleged, [the accused] had sexual intercourse with [the complainant],
without [the complainant’s] consent,
knowing that [the complainant] did not consent.
Generally, proving sexual intercourse is the easy part. I haven't watched the series but from the Wikipedia synopsis, it seems that this might not even be contested. So the Crown only need to prove the last two elements if the first is admitted.
Consent involves a conscious and voluntary agreement on the part of [the complainant] to engage in sexual intercourse with [the accused]. It can be given verbally, or expressed by actions. Similarly, absence of consent does not have to be in words; it also may be communicated in other ways such as the offering of resistance although this is not necessary as the law specifically provides that a person who does not offer actual physical resistance to sexual intercourse is not, by reason only of that fact, to be regarded as consenting to the sexual intercourse … [see repealed s 61R(2)(d) Crimes Act 1900]. Consent which is obtained after persuasion is still consent provided that ultimately it is given freely and voluntarily.
and
The Crown must prove to you, beyond reasonable doubt, that [the accused] knew that [the complainant] did not consent.
You might ask how the Crown can prove that [the accused] was aware that [the complainant] did not consent without an admission from [him/her]. The Crown asks you to infer or conclude from other facts which it has set out to prove, that [the accused] must have known and that [he/she] did indeed know … [deal with the relevant evidence].
In a situation where [the complainant] does not in fact consent, [the accused’s] state of mind at the time of the act of intercourse might be that [he/she] actually knew that [the complainant] was not consenting. That is a guilty state of mind. If the Crown satisfies you beyond reasonable doubt that that was the state of mind of [the accused] at the time of the act of intercourse, then the third element of the charge has been made out.
On the other hand, you may decide on the basis of the evidence led in the trial [or if applicable and relied upon by the accused] that [the accused’s] state of mind might be that [he/she] genuinely, though wrongly, believed [the complainant] was consenting to intercourse. That is not a guilty state of mind. It is for the Crown to prove that [the accused] had a guilty mind, and so if the Crown has failed to prove that, at the time of intercourse, [the accused] did not genuinely believe that [the complainant] was consenting, then you would have to say that this third element of the offence is not made out, and return a verdict of “not guilty” of this charge … [refer to relevant arguments by the parties].
