If the underlying holdings are the same, how would the tax liability differ?
As far as I understand, it would not.
But a actively managed fund usually will have a much higher turnover rate, meaning the buying and selling of holdings in the protflolio as they adjust to the managers intention, the taxes of those sales could be passed on to the investor. This would not be on the sale if the etf or fund, rather while the investor is holding the fund.
Even passively managed index funds can have higher turnover rates, depending on how they are weighted. But on average I believe actively managed funds have a much higher turnover rate.