I don't know of any narration or anything that would directly address what you are asking. Likely there isn't. Simply said, men should act fairly among their wives. So my answer is basically my understanding by putting pieces together.
There are things to consider though. Say you are marrying the princess of England and at the same time you are marrying a poor lady from the slums of the worst country of the world named.
I think that giving these 2 people the same mahr may be deemed disrespectful. As in Islam عُرف norms are important. I mean if you are marrying a super rich girl, then her family's quality of life is different than others and Islam respects that. (In Islam you can't marry a rich girl then tell force her to live in a slum)
Though I think history can help us to better asses this. The mahr at the time of the prophet was very very limited. It wasn't that the mahr was something like $1000-100000 as it is nowadays. The range was much more limited. (We have narrations that indicate the best of wives are those who ask little for their mahr, the best of wives are those who free their husbands of their mahr...at the same time we have that the best of husbands are those who give their wives their mahr as soon as they can)
From Imam Sadiq: The prophet wives and never had a mahr more than 12 uqiyah and nash ; uqiyah was 40 dirham and nash was 20 dirham. So they couldn't have been more than 500 dirham (~50 dinar).
Also when Ali married Fatimah he only sold his shield for no more than 500 dirham.
500 dirham is almost 170 gr of gold. In today's world it's worth roughly $6700.
My point is the range of Mahr at the time of prophet wasn't that much. Today mahr can be significantly different. Back then perhaps providing one wife with 1-10 more dinars wasn't that much of a big deal. Today the range is so substantial that the differences would become bold.
But more than mahr is the treatment. I mean what good would a high mahr be if the husband treats this wife worse? He should treat them both with the same level of joy, it shouldn't be that the first lady would get 100% of his attention, love, commitment and the 2nd lady because of having a mahr of 1/10th of the other she would get less commitment. Likely these 2 wives are hard to marry/satisfy at the same time unless there is something to balance them as in the husband would bring the poor lady to higher social status.