You say that as if they're mutually exclusive, but they really solve two separate problems.
If you have a monopsony on labor (note that this is not very common for unskilled labor; think company towns), it means that people are being compensated unfairly, in the same way that monopolies overcharge customers unfairly.
But even if you don't, there may be people whose fair market wage isn't enough to live on. Even if there are thousands of employers who need unskilled labor, it's still possible for the supply to outstrip the demand, which is the exact scenario that a UBI works well for -- the market wage may be $4/hour, but supplemented by a UBI it's enough to live on. Meanwhile in the same circumstances some other policies, like minimum wage, do the opposite -- when there is a glut of labor, price controls increase unemployment and make the problem worse, because then people don't get $4/hour plus a UBI, they get to collect unemployment until it runs out and then starve to death.