In Islam, if a woman commits adultery, a man can use Li'aan and use it to inflict the punishment of hud on her. If she tells a lie, she also has to say in the end that she may be cursed by Allah. But at the same time, a woman cannot do so.
Now if a man were to rape a woman, she cannot go to the court and get him stoned without four witness. Even if there is a punishment of tazir, he still has less punishment than a woman who cheated on her husband and got caught.
In general any person can not accuse another of fornication\adultery without providing evidence (four witnesses). Indeed an accusation without evidence is itself a crime which incurs a punishment for the accuser (Quran 24:4).
However, Li'aan is an exception prescribed in the Quran 24:6-9 whereby a husband who sees the act can accuse his wife without requiring four witnesses. The wife can either confess or deny this accusation under oath. In case of denial she does not get punished for adultery nor does the husband get punished for slander - and the two are separated and any children born of the alleged adultery are disowned by the husband.
A husband can initiate Li’aan while a wife can not. This is not unfair, rather it is fair because men and women are biologically different and zina has different implications for them. Li’aan serves a valid personal interest for a husband while it would not serve any such interest for a wife:
If a wife engages in adultery:
It breaches the husband's rights since in Islam a husband has exclusive sexual right over the wife.
Any children born from adultery would be falsely considered the husband's own. They would be called by his name. He would be responsible for their housing, feeding and other financial support. They would also have inheritance rights from his property. Making a husband give his wealth to another man's children is clearly unjust. Hence a legal remedy is needed.
On the other hand if a husband commits zina:
A wife does not have exclusive sexual right over the husband, because polygamy and concubinage are permissible in Islam. So while a male adulterer commits a sin he does not violate the right of his wife.
Any children born of the zina would be delivered from the womb of the fornicatress and not the wife - therefore, there is no possibility of the child being falsely attributed to the wife. A wife is also not responsible for housing, feeding or any other maintenance of the husband's children nor do they inherit from her. So she does not suffer any harm.
In your second paragraph you have drawn a comparison with the requirement of evidence for rape.
The Islamic laws on rape are covered here: What are the Islamic rulings on Rape? and here. Evidence is always necessary for enforcing legal punishments, and it is common sense that a person can not be punished based on an accusation alone. Li'aan is not different from rape in this regard: the female is not punished if she denies the allegation as mentioned in verse 24:8.
Secondly: Men too can be victims of rape and would face a similar situation and hence this can't be used to contrast the laws for men and women.
شهد الله أنه لا إله إلا هو والملائكة وأولو العلم قائما بالقسط لا إله إلا هو العزيز الحكيم
Allah witnesses that there is no deity except Him, and the angels and those of knowledge - maintaining in justice. There is no deity except Him, the Exalted in Might, the Wise.
Allah is Al-Muqsit, "The Fair, The Just". It obviously follows that Allah's Law is also fair and just.
People are fallible.
Most of what people call "Islamic Law" is just human attempts at interpreting and applying Allah's Law. Without divine infallibility there is no guarantee that it was interpreted perfectly or that a judge makes no mistakes in their judgment, so attributing any unfairness to Allah or Islam is presumptive.
That said, there is also no guarantee of "equality" between men and women. Men and women are not the same, gender roles are well-established in Islamic jurisprudence, and Islamic law explicitly accounts for this. There will always be laws and rules which apply to men but not women, or vice-versa.
There is also no guarantee that everything will be fair in this world; any worldly injustices will be reconciled on the Day of Judgement. This includes people who escape worldly justice as much as any who are unjustly punished: All will be known and accounted for.
