Thank you for the update!
Do you happen to know if there are quality comparisons somewhere, between llama.cpp and exllama?
Also, in terms of VRAM consumption, are they equivalent?
oobabooga recently did a direct perplexity comparison against various engines/quants: https://oobabooga.github.io/blog/posts/perplexities/
On wikitext, for llama-13b, the perplexity of a q4_K_M GGML on llama.cpp was within 0.3% of the perplexity of a 4-bit 128g desc_act GPTQ on ExLlama, so basically interchangeable.
There are some new quantization formats being proposed like AWQ, SpQR, SqueezeLLM that perform slightly better, but none have been implemented in any real systems yet (the paper for SqueezeLLM is the latest, and has comparison vs AWQ and SpQR if you want to read about it: https://arxiv.org/pdf/2306.07629.pdf)