Personal opinion...
Note 2 has
- Larger battery capacity.........and it seems that Note 2 somehow has extremely good battery life, better than the usual samsung phones. no idea why though.
- Bigger screen (Subjective).......also, note 2 bezel and sides seem to curve better to fit the palms as compared to the relatively sharp edges of s4 which is similar to iphone 5 (oops)
- S-Pen functionality (usefulness depends on individual) .... might be very useful for ppl who take notes and conference call at the same time.
- Significantly cheaper
S4 has
- Newer version of android/samsung touchwiz, hence more features (usefulness depends on individual, Note 2 will get it eventually) .... many of us find the new features gimmicky. I do too, except for maybe the 'finger' air view instead of using a stylus for preview, the more camera features (e.g. eraser) and smart pause. There is also a new layout for the camera features but i prefer the older, traditional layout of Note 2.
- Higher resolution display ........ quite impossible to discern the difference for most of us unless you very very intentionally zoom in, as both screens have high ppi. I cannot really rmb but i think note 2 has a better arrangement of pixels.
- More powerful processor (irrelevant in day to day usage) ... in fact, note 2 seems to have less lag, possibly due to better optimization and older version of touchwiz.
- Higher megapixel camera....
That being said, this does not mean that Note 2's software is inadequate, or processor is slow and sluggish, nor does it say that the S4 battery life is bad. The unmentioned qualities are more of expected average while the highlighted ones are the main advantage one has over the other.
