The point is not simply to give people more money (though in some countries that might not be a bad idea), but to ensure that they don't lose that money if their situation changes. Often it's more attractive to remain completely unemployed than to work part time at minimum wage. With UBI, every bit of paid work you do, leaves you better off financially. It removed disincentives to work, because working people get it too. The costs of UBI are easily balanced with taxes. And because you don't have to qualify for it, you can save a lot on bureaucracy; it leaves people at the bottom of the economic ladder with a lot more freedom in their lives.
For means-tested programs, you can replace means-testing with unconditional benefits and appropriate progressive tax rate changes, and acheive exactly the same effects (modulo differences in definitions of income, but is there really a big benefit there?) while eliminating duplicate bureaucracy. Most UBI proponents don't prefer as rapid of a claw-back (which sometimes exceeds 100% in some ranges) as the aggregate of existing means-tested welfare programs, and would instead claw-back at a slower rate but extend the claw-back higher up the income distribution so that the drag is on the rich rather than the lower middle class, to improve upward mobility compared to existing means-tested welfare, but if you wanted to optimize only for bureaucratic efficiency without moving the claw-back higher up the income distribution and keeping it below a 100% marginal rate to eliminate perverse incentives, you could do that with UBI and tax changes, too, and still have a (smaller) net win.
I have no idea whether that's enough to make up the difference.
UBI doesn't really make sense as a replacement for unemployment insurance, unless benefits are really high. If you replace UI with a poverty-support-level UBI, it makes unemployment a lot worse for anyone but the lowest-paid workers.
UBI might reduce the perceived need for public funding of additional unemployment benefits in extended downturns (though if the be benefit level is poverty-support-level, probably not that much; that's more of a support for middle-income dislocation.)