Whose side are you on, New Yorkers?

Do you want to raise New York City income taxes on rich people to start full-day prekindergarten classes for every 4-year-old in the five boroughs?

Or would you rather see Albany whack taxes and at the same time use existing money in the budget to launch pre-K classes everywhere in the state -- from Staten Island to Niagara Falls?

We strongly favor the second option, but not everyone agrees. The dueling questions met head on in a noisy but telling collision Monday as Gov. Andrew Cuomo and Mayor Bill de Blasio held simultaneous news conferences.

Surrounded by a cheering squad of union honchos in East Harlem, de Blasio called for a groundswell on behalf of his plan to create a citywide pre-K program that sticks residents making more than $500,000 a year with the tab.

Surrounded by a crowd of business boosters and budget gurus in Albany, Cuomo inveighed that New York State for too long has been regarded as a high-tax, anti-business state that spends far more than it earns.

Cuomo has avoided putting himself directly at odds with de Blasio, but the smart money is betting that no specific pre-K tax will be imposed. Cuomo refused to discuss the matter Monday. Assembly Speaker Sheldon Silver and State Senate co-majority leader Jeffrey Klein support the de Blasio scheme, which Albany would have to ratify.

The good news is that both factions in this odd skirmish want to expand pre-K. If you get children off to a solid start, they stand a much better chance of doing well later in their academic careers.

But in trying to give all city children a shot at pre-K, the mayor also seems intent on proving his progressive bona fides to unions and other supporters.

Why else would he plead for a tax hike on his richest constituents -- when Albany may offer a broader plan that doesn't contain a tax increase?

Why else would he forgo a chance to move the city and state forward with pre-K while cutting state taxes?

De Blasio's plan has more losers than winners.