In this work, we investigate the effect of language models (LMs) with different context lengths and label units (phoneme vs. word) used in sequence discriminative training for phoneme-based neural transducers. Both lattice-free and N-best-list approaches are examined. For lattice-free methods with phoneme-level LMs, we propose a method to approximate the context history to employ LMs with full-context dependency. This approximation can be extended to arbitrary context length and enables the usage of word-level LMs in lattice-free methods. Moreover, a systematic comparison is conducted across lattice-free and N-best-list-based methods. Experimental results on Librispeech show that using the word-level LM in training outperforms the phoneme-level LM. Besides, we find that the context size of the LM used for probability computation has a limited effect on performance. Moreover, our results reveal the pivotal importance of the hypothesis space quality in sequence discriminative training.