In fact, both Switch iterations uses a 16Wh battery. Even the Switch Lite, which boasts a slightly better battery life than the first generation Switch, has a smaller battery, rated at 13.6Wh. Instead, Nintendo is using a more efficient processor to improve the battery life of the Switch. The circuit board in the updated Switch is also codenamed MODIN, likely referring to a modified ODIN. The latter is the name of the board on the first generation Switch.
Last month, the FCC filings have already indicated that the slight upgrade included a new chipset, alongside a better battery life. In hindsight, this may have been obvious, as there was no mention of a new battery during the initial report. The updated Nintendo Switch as well as the Switch Lite will be on shelves in August, and starting 20 September, respectively. As of now, it also appears that they will land on our shores at the same time as the international market. (Source: US FCC [1], [2] via The Verge)