Like you, i am deciding b/w G2 and 5S. Note 3 is too big since i already think that my Note 2 is too big. In addition, i hate SAMOLED screens outside! I absolutely think that Samsung should junk SAMOLED forever! Useless under the sun!
The problem with G2 are two folds. Display is OK, not class-leading...but you guys heard enough from me about that!
The other issue is LG. LG does NOT have a good record of updating their phones post-sales.
I would buy G2 instantly IF i knew better about LG's update plans. For example, it would be tremendous if LG CEO would announce that they will keep their G2 (and subsequent flagships) up to date as much as possible. That is all i need...a verbal commitment on their end that they will TRY to keep their phones updated.
LG Optimus G got Jellybean...but no word on 4.3. Samsung and HTC already have published their full intention on giving 4.3 to their flagship phones in October. But where is LG in all this? No where to be found. Dead silent.
LG G2 will have 4.2.2 when it comes out. No word from LG about 4.3. In 2011, LG guaranteed ONE update for your phone. One. On a 2 year contract. One. So, that means that G2 will probably get 4.3 later this year or early next year...and that's it. If you're lucky, then maybe 4.4 (KitKat) mid 2014 or later...which is likely 6-12 months behind the official release.
Remember, after G2 comes out, LG is already working on Optimus PRO 2, which should come out next February. So, they don't have much time (and resources?) to work on G2 updates. It is a vicious cycle. And once Pro2 comes out, they are working on G3. etc.
Although Google piece-meal their updates nowadays thru PLAY Store, it is still nice and advantageous to have software updates. I am not sure if i can sit on 4.3 for two years while Nexus (and Samsung?) phones are on Kitkat and beyond. That would stink IMHO.
If i were to stay on Android, then i would wait until next month when Google hopefully will announce the Nexus 5. Recent leaks show that N5 will be quite a powerhouse, made by LG. It will have most (if not all) G2's stuff, but without the heavy UI and (controversial) buttons.
For me though, i am leaning towards iPhone 5S. My Note 2 will go to my son as a gaming device, which is great with the big screen. Apple copied some stuff from Android (and Windows) and made it better. Apple is like Toyota...they are slow in adopting stuff, but when they do, it usually runs perfect...see Facetime and iMessage. And since iOS7 has most of the important stuff of Android (like notification, quick settings, etc.), i won't miss Android too much by switching. With iOS, the software (and hardware) runs smoother. Camera from iPhones tend to be very well done...but G2 camera is mighty impressive though.