Side-channel attacks (SCA) focus on vulnerabilities caused by insecure implementations and exploit them to deduce useful information about the data being processed or the data itself through leakages obtained from the device. There have been many studies exploiting these side-channel leakages, and most of the state-of-the-art attacks have been shown to work on systems implementing AES. The methodology is usually based on exploiting leakages for the outer rounds, i.e., the first and the last round. In some cases, due to partial countermeasures or the nature of the device itself, it might not be possible to attack the outer round leakages. In this case, the attacker has to resort to attacking the inner rounds. This work provides a generalization for inner round side-channel attacks on AES and PRESENT, and experimentally validates the same for AES with non-profiled and profiled attacks. We formulate the computation of the hypothesis values of any byte in the intermediate rounds of both AES and PRESENT. The more inner the round is, the higher is the attack complexity in terms of the number of bits to be guessed for the hypothesis. We discuss the main limitations for obtaining predictions in inner rounds and, in particular, we compare the performance of Correlation Power Analysis (CPA) against deep learning-based profiled side-channel attacks (DL-SCA). We demonstrate that because trained deep learning models require fewer traces in the attack phase, they also have fewer complexity limitations to attack inner AES rounds than non-profiled attacks such as CPA.