And there is the one XL
With jellybean running on all phones, I doubt you will see a
huge difference in speed and smoothness across the note II, GS 3, one X/X+/XL, S4 powered handsets will feel more snappy and instant when loading apps, game levels, gallery thumbnails etc. due to a number of reasons such as having way more performance per core than the exynos quad core (android and apps don't fully utilise dual core let alone quad yet so the greater performance per core is more of a benefit than an additional 2 cores amongst other reasons)
Battery life wise, the one X+ and XL are very good (X+ seems to have a problem at the minute with drain whilst idle, but am sure that will be fixed soon.....). None will be anywhere near the note II levels though.
Jellybean has improved the one X as well in a number of areas including battery life (although won't be as good as the X+ and XL), the performance is even better than the GS 3 running JB surprisingly (in benchmarks)
Posted some pros and cons of the phones in another thread:
Instead of the one X, I would look at the X+ (bigger battery, better front camera, 64GB internal storage and has JB/sense V4+) or XL (LTE support, better CPU thus better performance and battery life) instead.
If you are sure that size isn't an issue, then the note II, if it is then I would decide between the X+ and XL.
Main advantages of the note II (some apply to the GS 3 as well) over the X+ and XL is:
- battery life
- screen size
- 1080P recording
- SPEN
- 2GB RAM
- better CPU chipset than the X+
- NLED
- SD slot
Main advantages of the X+ and XL over the note II:
- screen quality
- build/perceived quality
- X+ has 64GB internal storage (XL is only 32GB), both have no SD slot
- XL has the better CPU chipset
audio is more or less the same, design is personal preference and software skin is personal preference.
The camera for photo quality is more or less the same on all the phones, some shots look better on the note II whilst other shots look better on the X+/XL, both have plenty of features/options (hopefully the GS 3 will get some of the camera/gallery features from the version of touchwiz on the note II), but one series/sense has more stuff overall and the camera UI is better (IMO)
Screen is also personal preference, but many people and review sites still class the SLCD 2 IPS screen as being king, but many people prefer the SAMOLED panels due to blacks, infinite contrast ratio, vibrant colours so games and videos look amazing.
I personally wouldn't bother with the GS 2 or note now.
Best to have a play with them for yourself and see which one you prefer.
If it where me and size wasn't an issue and you don't mind touchwiz, then the note II, if size is an issue and/or you don't like touchwiz and you don't need more than 32GB internal storage then the one XL, if storage is an issue then the X+
The one S is another alternative, for some people, the downsides of it compared to the X+, XL are:
- screen isn't 720P and not as big but is still superb overall, don't let all the pentile talk put you of, judge yourself in some shop but not beside the XL/X/X+ as it will look pretty poor then

The only thing I want is a bigger screen

- 16GB internal storage (10GB for videos, photos etc. and 2.21GB for apps)
- crap NLED
Everything else is as good as the X/XL and in some areas better i.e.
- CPU chipset same as the XL, so superb and second best to the the S4 pro in the N4
- audio is amazing, second best to the GS 3, although some say the one S audio sounds better, doubt there will be much difference though
- camera same as the X/XL/X+, however, 1080P videos look much better in terms of smoothness and light metering
- aluminium uni-body, which IMO feels far nicer than all the phones especially the black model which has been micro arc oxidised (but some people have had chipping issues with it, however, HTC released an updated design with smoother edges that has fixed the problem, the grey model doesn't have any problems)
- battery life is amazing, only beaten comfortably by the note II, slightly better than the GS 3 and way better than X on ICS (need to see more battery stuff when more people get JB). Plus if you really want you could fit the 2100mAh from the one X+ into the phone
However, there are 2 models floating around, 1 with a S3 chipset (old gen) and nowhere as good as the S4 chipset, mainly in the performance and power efficiency areas. S3 CPU has a clock speed of 1.7GHz and S4 CPU has a clock speed of 1.5GHz.
Regarding screen size, the bigger the better IMO, however, only if the phone is comfortable to hold and easy enough to use with one hand so no bigger than the HTC DNA for me. The GS 3 is very comfortable in one hand (still not the easiest to navigate the entire screen with one hand though) compared to the X/X+/XL despite being slightly larger.