In principle, both pQED and scQED will generate identical results under the complete basis limit. Compared to scQED, the pQED scheme is much simpler in the sense that it does not require additional re-development of electronic structure theory for the QED Hamiltonian as well as the simplicity that comes with a non-self-consistent solution. Despite the enormous recent progress in sc-QED and pQED schemes, what is generally missing is a consistent comparison of both approaches and assessment of the strengths/limitations of each method under different scenarios. In particular, an open question in the field of ab initio polariton chemistry is whether a pQED calculation can provide the same level of accuracy compared to the scQED simulation. In this work, we use the pQED approach to compute polariton properties and directly compare to the existing work based on the scQED approaches. We will directly assess the accuracy of the pQED approach by computing the eigenspectrum of the polaritonic system. Further, we also present new theoretical metrics to analyze the excited state properties of the molecule-cavity hybrid systems, which will be a valuable tool to understand how forming polaritons can influence the excited state properties of the molecule. Finally, we will investigate how forming polaritons can influ-ence the fundamental property of molecules, including dramatically changing the excited state character of the polyphenyl ether (PPE) molecule, as well as compute the polariton eigenspectra and absoprtion spectra of coupling a single-walled carbon nanotube (SWCNT) that contains ∼1000 carbon atoms with an optical cavity.