It would cost considerably less and thus higher taxation would be less of a concern (as a way to stifle more money from the rich to the poor).
Do you still like the idea if it's more expensive rather than less?
I think the difference would be in the efficiency and simplicity of such a system. Currently, the U.S. spends over a trillion dollars on state and federal welfare programs (spread across 126+ programs). However, the government spends it quite poorly and in many indirect ways. Giving them a cheque would certainly be better.
You're right in that it could actually be more expensive. I'm not sure what my stand on the subject would be in that case. Even with my libertarian beliefs, (and there are good arguments that basic income is perfectly compatible with libertarianism) I have to keep in mind of the realities related to the surging amount of poverty and that it's unsustainable.