To tack onto Karsten Theis's answer: Symmetry is inherently a qualitative tool, because it is binary. Two things (AOs) either have the same symmetry and can overlap, or they have different symmetry and can't overlap. But you can't say something is "more symmetric" and thus leads to "more overlap"; that would just be complete nonsense. So, symmetry tells you which lines to draw, but it doesn't tell you the extent of the overlap, i.e. how far up or far down the lines need to go to.
Formally, this is expressed in terms of integrals involving atomic orbitals $\phi_i$:
$$\langle \phi_1 | \hat{H} | \phi_2\rangle \begin{cases}
\neq 0 & \text{if }\phi_1 \text{ and } \phi_2 \text{ transform as the same irrep} \\
= 0 & \text{otherwise}
\end{cases}$$
The energies depend on exactly what this number evaluates to, and to find that out, you need to actually evaluate this integral (and many others). Conceptually that's not hard to do, because we know how to write the AOs $\phi_1$ and $\phi_2$, and we (kind of*) know what the Hamiltonian $\hat{H}$ is. And it turns out that it isn't too hard for a computer to perform this integration. There are various software packages that will do this sort of calculation for you. But doing it by hand is not feasible, especially for any non-trivial molecule, and that's why if you limit your approach to a symmetry-based one, you can only ever get qualitative information out of it.
Note that I'm not trying to equate the energy of the MO with that integral above. The expression for the energy will (in general) depend on many of those terms. (Exactly how? Well, the MOs are linear combinations of the AOs, or at least we postulate that they are:
$$|\psi\rangle = c_1|\phi_1\rangle + c_2|\phi_2\rangle + \cdots$$
so the energy associated with the MOs is
$$\begin{align}
E &= \langle \psi | \hat{H} |\psi\rangle \\
&= \langle c_1\phi_1 + c_2\phi_2 + \cdots | \hat{H} | c_1\phi_1 + c_2\phi_2 + \cdots\rangle \\
&= c_1^*c_1\langle\phi_1 | \hat{H} | \phi_1 \rangle + c_2^*c_1\langle\phi_2 | \hat{H} | \phi_1 \rangle +
c_1^*c_2\langle\phi_1 | \hat{H} | \phi_2 \rangle +
c_2^*c_2\langle\phi_2 | \hat{H} | \phi_2 \rangle + \cdots
\end{align}$$
Yeah, you don't want to do that by hand. And actually finding those coefficients $c_i$ is an entirely separate problem which involves similar considerations.)
* There is a "slight" problem, in that the electron–electron repulsion term in $\hat{H}$ depends on the electron distribution which in turn depends on the form of the MOs. But that's a technical detail. You can worry about it if you're actually writing computer software to do those integrals.