Arabic is a Semitic language which is widely spoken with many dialects. Given the success of pre-trained language models, many transformer models trained on Arabic and its dialects have surfaced. While there have been an extrinsic evaluation of these models with respect to downstream NLP tasks, no work has been carried out to analyze and compare their internal representations. We probe how linguistic information is encoded in the transformer models, trained on different Arabic dialects. We perform a layer and neuron analysis on the models using morphological tagging tasks for different dialects of Arabic and a dialectal identification task. Our analysis enlightens interesting findings such as: i) word morphology is learned at the lower and middle layers, ii) while syntactic dependencies are predominantly captured at the higher layers, iii) despite a large overlap in their vocabulary, the MSA-based models fail to capture the nuances of Arabic dialects, iv) we found that neurons in embedding layers are polysemous in nature, while the neurons in middle layers are exclusive to specific properties