Nitrous oxide is a much more powerful greenhouse gas than methane - 298 times more powerful than carbon dioxide over a 100 year timeframe on a per tonne basis.  See What is Global Warming Potential?
Fortunately, the absolute amount of nitrous oxide emitted from agriculture is lower than methane. In New Zealand, most nitrous oxide is produced by the action of soil bacteria in urine patches in paddocks.  Smaller amounts come from dung deposited during grazing, stored manures spread back onto pasture, and from nitrogen fertilizer.