Worst-case time algorithm?...which one is faster?
If $g(n) = \Omega(f(n)\log n)$ then for large $n$, $g(n) \geq Cf(n)\log n$ (for some $C &gt; 0$, and so algorithm $B$ takes more time than algorithm $A$ (in the worst case). In other words, algorithm $A$ is faster.

If $g(n) = O(f(n)\log n)$ then all we know is that for large $n$, $g(n) \leq Cf(n)\log n$; it could be that also $g(n) = \Omega(f(n)\log n)$, in which case algorithm $A$ is faster; or it could be that $g(n)$ is constant while $f(n) = n$ (for example), in which case algorithm $B$ is faster; and there are other possibilities.

If $g(n) = \Theta(f(n)\log n)$ then in particular $g(n) = \Omega(f(n)\log n)$, and so we revert to the first case.