The Maritime Self-Defense Force's stealth frigate JS Mogami. Japan is trying to sell its Mogami-class warships to New Zealand. | Bloomberg Japan’s stealthy and highly automated Mogami warship is set for a showdown with the simpler and less expensive Type 31 frigate from the U.K. as the two nations compete to supply vessels to the Royal New Zealand Navy. New Zealand said last week it was looking at both options to replace its two aging Anzac-class frigates, which were commissioned almost 30 years ago. The Defense Force is set to report on the rival offerings by the end of next year, at the latest, and the government hasn’t ruled out buying more than two. For Japan, a deal with New Zealand would build on an agreement signed recently with Canberra to build the first three of 11 Mogami-class ships planned for Australia. That deal is Japan’s first major export order for lethal weaponry since World War II and comes as Tokyo seeks to develop its defense sector through foreign sales.…