I think most of the one X problems have been sorted out with the newest batches and software updates now. However, it should be the X+ or XL to decide on, not the original X IMO. XL has the far better CPU chipset thus better performance and better battery life, also supports LTE and has all these
advantages over the tegra 3 based devices.
The X+ has the bigger battery, more internal storage (64GB), better front camera, jellybean out of the box, overclocked CPU.
Plus afaik these devices don't have any of the issues that the normal X had/has.
The nexus 4 is pretty much top dog now, largely due to its price.
Main advantages of the n4 over the GS 3
- far better CPU chipset
- 1GB more RAM (LTE model of GS 3 has 2GB as well though)
- sharper/clearer screen, whites are much whiter
- build and perceived quality
- nexus device so will get updates fast and be guaranteed to get them
- price
Main advantages of GS 3 over the n4:
- 1080P recording
-
more screen space
- better viewing angles, blacks are black, colours are saturated
- SD slot
- better audio
The camera for them (regarding photos) all look to be more or less the same, some perform better in certain scenarios than other devices. Sense V4/HTC devices have the better UI IMO and it just works better, also have way more features than the GS 3 and N4.
Another option to consider is the note II, if you can handle the size and don't mind touchwiz as well as the price tag
With all devices running JB, there won't be a huge difference in real world performance, not enough to worry about anyway.
The battery life of the nexus 4 is very good, however, you need to turn some things of at the minute as there is a software/driver problem that is making the battery awful, but once that is sorted it should be the best (aside from the note II, RAZR maxx etc.), S4 pro=most power efficient chipset + screen=supposedly very PE + a next gen 2100mAh battery with optimised software =
Coming down to the XL, X+, X, GS 3 and N4, the devices that I would be looking at would be the
N4 and XL