First, when one half of a heterosexual married couple dies, the deceased spouse's assets transfer tax-free to the surviving spouse, and no tax is due (if at all) until the death of the second spouse. However, no such benefit exists for same-sex couples--not even for same-sex couples legally married in other states. Many people incorrectly believe that NY recognizes same-sex marriages performed in other states. Granted, in many ways NY does recognize such marriages, but thanks to DOMA it does not recognize married same-sex couples when it comes to estate taxes.
Second, same-sex couples are treated unfairly when it comes to the generation skipping tax (GST). In a nutshell, the GST is levied against assets that pass from one generation to a generation two or more levels below the original generation (i.e., gifts from grandparents to grandchildren). The general purpose (put very succinctly to avoid your eyes from glazing over) is to avoid assets transferring tax-free. The main point here is that heterosexual married spouses can transfer assets tax-free between them, regardless of their age difference (i.e., even if they're more than a generation apart in age). However, for same-sex couples, due to the GST, if the age difference between the same-sex partners is 37.5 years or more, the GST will be levied against the surviving partner. This scenario might not apply to the majority of couples, but it is an unacceptable inequality nonetheless.
Tax equality might not be a glamorous reason for why marriage equality is necessary, but it's a very important one. Without marriage equality there are two classes of (otherwise nearly identical) tax payers New York. If marriage equality doesn't happen today (the last day of the legislative session) then the battle must go on when the legislature reconvenes.