It depends on the notebook. In general, Linux is much more efficient than Windows (much less bloat), so in theory it should automatically lead to better battery life, However, on some (or even a lot of) notebook models, there are all sorts of weird manufacturer hardware choices, UEFI settings and whatnot which don't always fully conform to specifications or have other quirks which the proprietary Windows drivers for that device circumvent and thus deal with in a way that leads to the intended positive result, but the open-source Linux drivers which usually follow the specifications will then lead to a negative result (usually: less power efficiency => increased battery drain). So it's best to stick to notebook models and manufacturers which are known to be good devices for running Linux on them (or where the manufacturer even directly supports running Linux on), and not blindly or randomly buy a notebook hoping that Linux will run at 100% efficiency on every weird hardware combination.