Software Engineering is a branch of computers that includes the development of structured software applications. Estimation is a significant measure of software engineering projects, and the skill to yield correct effort estimates influences vital economic processes, which include budgeting and bid tenders. But it is challenging to estimate at an initial stage of project development. Numerous conventional and machine learning-based methods are utilized for estimating effort and still, it is a challenge to achieve consistency in precise predictions. In this research exploration, various ANN-based models are compared with conventional algorithmic methods. The study also presents the comparison of results on various datasets from the artificial neural network models, deep learning models, higher-order Neural Network models, leading to the conclusion that hybrid methods yield better results. This paper also includes an analysis of primary data collected from Software Project professionals using the questionnaire method involving questions related to software cost estimation.