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Comparing wavefunction-based methods and density-based methods for quantum mechanical calculations, how is "rank" determined?
For example, in wavefunction methods, CCSD(T) is considered a higher level than MP2, which is a higher level than HF.
For single reference wavefunction based methods, the comparison is relatively straightforward within method "families". This is due to the nature of how these methods are formulated, usually involving a very long series that has been terminated at some point to make the calculation feasible.
You start with Hartree-Fock, which ignores electron correlation. After that you can add perturbative corrections of increasing order (this will be the MP2, MP3, MP4, MPn family), do something called configuration interaction, truncated at increasing levels of excitation (CIS, CISD, CISDT,...,FCI), or something called the coupled cluster methods, again truncated at some level of excitation (CCSD, CCSDT, CCSDTQ,...,FCI).
In these cases the most straightforward interpretation of "higher level" would mean a less aggressive truncation of the series that includes more terms. In case of CI and CC, this almost always results in more accurate results, and both converge to the same limit, where all possible terms are included and correlation effects are exactly calculated. (of course there are errors from other approximations) The MPn perturbation series has no such strong guarantees, and this is one of the reasons why pretty much noone uses anything beyond MP4 these days. (even MP4 is seldom used)
For DFT you have something called Jacob's ladder, but things are generally more murky, as most DFT functionals have many empirical (fitted) parameters, and there is no straightforward way of comparing them.
In general, the only way to compare them, is to take a big database of either experimental or calculated (via CCSD(T) or similar high level method) data, and compare the average/maximum errors.
If you want to solely know about DFT functionals, read about Jacob's ladder of functionals. There's a good recent review of a slew of DFT functionals: http://dx.doi.org/10.1063/1.4948636
I do not think hybrid functionals are higher in theory. All that is being done is mixing exact exchange with other functionals that have already been established. But I think some people may argue that is not the case.
Another thing that you may want to look at are the "plus methods": DFT + GW, DFT + U, DFT + DMFT. These methods add a term to the Hamiltonian to correct errors or capture behavior that cannot be observed with traditional DFT.
Most comparisons between DFT and Post-Hartree Fock Methods are done by comparing calculation results. And this comparison is not very straightforward. Usually physical values (e.g. binding energy, bond lengths) are calculated by different method and compared to experimental values. Usually, however, wavefunction methods are deemed to be more accurate or consistent. So they are often used as benchmarks for DFT calculations.
Aside from the used method, you should also pay attention to the used basis set. Generally, the larger the basis set the better the results. (This is strictly speaking not true, as just having a "large basis set" does not guarantee the additional basis functions are helpful. But usually basis sets are optimized to achieve maximum quality with a given number of basis functions.)
When comparing methods of different levels of theory, you should use a basis set of same quality. This will ensure the differences are really due to the method. In extreme cases a cheap method with a large basis set may give better results than a higher level method with a small basis set.
However, one should be careful with the "basis set of same quality" formulation, especially for DFT where thing are generally more fuzzy.
