Despite being widely spoken worldwide, Bengali and Hindi are low-resource languages. The state-of-the-art in modeling such languages uses BERT and the Wordpiece tokenizer. We observed that the Wordpiece tokenizer often breaks words into meaningless tokens, failing to separate roots from affixes. Moreover, Wordpiece does not take into account fine-grained character-level information. We hypothesize that modeling fine-grained character-level information or interactions between roots and affixes helps with modeling highly inflected and morphologically complex languages such as Bengali and Hindi. We used BERT with two different tokenizers - a Unigram tokenizer and a character-level tokenizer and observed better performance. Then, we pretrained four language models accordingly - Bengali Unigram BERT, Hindi Unigram BERT, Bengali Character BERT, and Hindi Character BERT, and evaluated them for masked token detection, both in correct and erroneous settings, across many NLU tasks. We provide experimental evidence that Unigram and character-level tokenizers lead to better pretrained models for Bengali and Hindi, outperforming the previous state-of-the-art and BERT with Wordpiece vocabulary. We conduct the first study investigating the efficacy of different tokenization methods in modeling Bengali and Hindi.