  The search for new \emph{ab initio} models rapidly delivering accurate
excited state energies and properties is one of the most active research lines
of theoretical chemistry. Along with these methodological developments, the
performances of known methods are constantly reassessed thanks to the emergence
of new benchmark values. In this Letter, we show that, in contrast to previous
claims, the third-order algebraic diagrammatic construction, ADC(3), does not
yield transition energies of the same quality as the third-order coupled
cluster method, CC3. There is indeed a significant difference in terms of
accuracy between the two approaches, as we clearly and unambiguously
demonstrate here thanks to extensive comparisons with several hundreds
high-quality vertical transition energies obtained with FCI, CCSDTQ, and CCSDT.
Direct comparisons with experimental 0-0 energies of small- and medium-size
organic molecules support the same conclusion, which holds for both valence and
Rydberg transitions, as well as singlet and triplet states. In regards of these
results, we introduce a composite approach that we named ADC(2.5) which
consists in averaging the ADC(2) and ADC(3) excitation energies. Although
ADC(2.5) does not match the CC3 accuracy, it significantly improves the ADC(3)
results, especially for vertical energies. We hope that the present
contribution will stimulate further developments and, in particular,
improvements of the ADC-type methods which have the indisputable advantage of
being computationally lighter than their equivalent-order CC variants.
