Despite a shared goal of expanding school choice, President Bush and Mayor Bloomberg’s proposals to help low-income children escape failing schools could clash.

The Bush plan would funnel public money into private schools through a voucher program, while the Bloomberg plan is an attempt to channel money into public schools.

At their face, the proposals look similar. Traditionally disadvantaged children would be given “backpacks” of public funding that would follow them if they transferred out of struggling schools. Under the Bush plan, however, students could take federal money with them to private schools, while the Bloomberg administration has touted its program — known widely as weighted student funding — as a way to redistribute city and state education dollars among public schools.

In his State of the Union address on Tuesday, Mr. Bush called for “giving families with children stuck in failing schools the right to choose someplace better,” which administration officials explained yesterday marks the revival of a proposal to give private school vouchers to low-income students in failing schools.

The city school’s chancellor, Joel Klein, who opposes vouchers, yesterday disclosed the details of a plan introduced last week by Mr. Bloomberg that aims to dismantle an inequitable city funding system through a new per-pupil funding formula.

“It would be driving real extra dollars into the system,” Mr. Klein said, referring to weighted student funding. “Over time, you’re trying to equalize those resources. That’s critical to what we’re doing.”

One thing the programs will most likely share is widespread opposition.

The Bush administration proposed the voucher program, which it calls “Promise Scholarships,” as a change to the federal No Child Left Behind act, which is up for reauthorization in Congress. But Mr. Bush’s voucher plans have had little success in earlier incarnations, something unlikely to change in a Congress now controlled by Democrats who have traditionally opposed vouchers.

The teachers union president, Randi Weingarten, yesterday reacted with fury to the mayor’s weighted student funding proposal. Under the old system, salaries for teacher positions — no matter how high or low — were covered by city funding sources. Under the new funding formula, schools would be funded based on the number of students at the school, with extra dollars for low-income students, English-language learners, and special-education students. Principals could choose to spend that funding on bringing in higher-paid teachers or on other resources or staff.

In fact, Ms. Weingarten said, such choices could lead to principals deciding against keeping more expensive teachers.

“The chancellor’s plan will hurt kids and educators alike because it will destabilize good schools and give principals a disincentive to hire experienced teachers simply because they cost more,” she said. “Schools with higher salary costs due to a stable, more senior staff would have less money left for other things like reducing class size and maintaining quality educational programs like art, drama, and music.”