So I found an article about it - when fed the same diet, they are about the same. However, it seems cattle are fed more dry food, which in turn produces more methane.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8357158/
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"There is a dearth of literature comparing the methane emissions between cattle and buffaloes fed on the same diet and maintained under similar environmental conditions. Our results revealed that the daily methane emissions were significantly greater in cattle than in buffaloes. However, this difference in daily methane emissions was attributed to the significantly greater dry matter intake and body weight in cattle (BW 538 kg; 10.5 kg DMI) as compared to buffaloes (BW 284 kg; 6.86 kg DMI). These results are in good agreement with a previous study [41], where a significant difference in enteric methane emission due to higher dry matter intake and body weight between cattle and buffaloes was reported.
The methane yield (g/kg DMI) between cattle and buffaloes in this study was not affected by the host species on the same diet and it was within the acceptable range of 12–30 g/kg DMI [42]. However, methane yield in both cattle and buffaloes were lower than reported by Charmley et al. [43] for high forage diet (>70%). The reason for the lower methane yield in this study could be attributed to the presence of tannins and saponins inhibitors in the Napier grass [44, 45], which are well known for lowering methane emission."
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8357158/
.
"There is a dearth of literature comparing the methane emissions between cattle and buffaloes fed on the same diet and maintained under similar environmental conditions. Our results revealed that the daily methane emissions were significantly greater in cattle than in buffaloes. However, this difference in daily methane emissions was attributed to the significantly greater dry matter intake and body weight in cattle (BW 538 kg; 10.5 kg DMI) as compared to buffaloes (BW 284 kg; 6.86 kg DMI). These results are in good agreement with a previous study [41], where a significant difference in enteric methane emission due to higher dry matter intake and body weight between cattle and buffaloes was reported.