How does the performance of QAOA and VQE compare to Grover's?

I believe finding the optimal solution is guaranteed for Grover's Algorithm along with quadratic speed-up according to Nielsen and Chuang's book.

I wonder if there is any statement regarding QAOA and VQE for the performance such as success probability or/and speed aspect.

In the paper in which QAOA is introduced, the authors state that "the depth of the circuit grows linearly with $$p$$ times (at worst) the number of constraints. If $$p$$ is fixed, that is, independent of the input size, the algorithm makes use of efficient classical preprocessing", (A Quantum Approximate Optimization Algorithm). Where $$p \geq 1$$ and the quality of the approximation grows with it.