Language modeling is a fundamental task in natural language processing, which has been thoroughly explored with various architectures and hyperparameters. However, few studies focus on the effect of sub-word segmentation on the performance of language models (LMs). In this paper, we compare GPT and BERT models trained with the statistical segmentation algorithm BPE vs. two unsupervised algorithms for morphological segmentation -- Morfessor and StateMorph. We train the models for several languages -- including ones with very rich morphology -- and compare their performance with different segmentation algorithms, vocabulary sizes, and model sizes. The results show that training with morphological segmentation allows the LMs to: 1. achieve lower perplexity, 2. converge more efficiently in terms of training time, and 3. achieve equivalent or better evaluation scores on downstream tasks. Lastly, we show 4. that LMs of smaller size using morphological segmentation can perform comparably to models of larger size trained with BPE -- both in terms of (1) perplexity and (3) scores on downstream tasks. Points (2) and (4) impact on sustainability of LMs, since they reduce the model cost: size and computation time. While (2) reduces cost only in the training phase, (4) does so also in the inference phase.

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