I would wait for more user comments on the one battery life who have owned the note II especially from here as you can't always be sure with the folks at XDA!

For browsing and anything that has white backgrounds displayed most of the time, generally LCD based phones will be better due to them being a lot more power efficient with whites, however, with blacks SAMOLED destroys LCD in power efficiency then since the pixels are essentially turned of, black uses the same amount of power as what white would on a LCD screen. And of course the HTC one is pushing a lot more pixels than the note II.
Anandtech's battery benchmark of the one compared to other phones (including note II):
http://www.anandtech.com/show/6747/htc-one-review/3
Here is gsmarena's comparison to the note II:
A lot of people have slated their endurance/stand by test, regardless of that, those don't really give any indication to real world usage. Signal is another extremely important point, if you have weak signal especially with poor coverage for a data connection then the battery life will drop very quickly regardless of how well known a device is for battery life and iirc the some people have said that their nexus 4 is not as good as the GS 3 etc. for that area (signal), Samsung, HTC and especially motorola phones seem to be pretty good. The HTC one sounds like it has very good signal (as shown on the previous pages) due to the antenna design.
and of course battery life can/will improve with more software updates for both devices.


For browsing and anything that has white backgrounds displayed most of the time, generally LCD based phones will be better due to them being a lot more power efficient with whites, however, with blacks SAMOLED destroys LCD in power efficiency then since the pixels are essentially turned of, black uses the same amount of power as what white would on a LCD screen. And of course the HTC one is pushing a lot more pixels than the note II.
Anandtech's battery benchmark of the one compared to other phones (including note II):
http://www.anandtech.com/show/6747/htc-one-review/3
Here is gsmarena's comparison to the note II:
and of course battery life can/will improve with more software updates for both devices.
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