Give an example of such a website . I don't notice such a problem yet

You need to buy the LTE version, which for now is not available yet. Rumours is the LTE model could probably be in only the next 2 - 3 weeks. LTE version model is i9505 while non LTE is i9500

You can use the S3/Note2 MHL adapter. Works perfectly. The older S2/Note MHL will not. Get it from any Samsung shops for rm109

I would say the battery usage is comparable but you wont get same SOT or usage hours since is only 2600 mAh vs 3100 mAh
EXAMPLE I was using 3g browsing for past hour continously n battery drop from 90% to 72% ie 18% /hour. On note 2 my average is 13 to 15%/hour
This is roughly quite similar
See battery drain chart : start time 2132 n end time 2234 : from 90 % to 72%
This is just a rough assessment
Definitely way much better than S3 which I used to see 25 to 30%/hour on 3g browsing

Omega taken down his rom. Brood rom cannot n fail install. Both these roms develop without any recovery known yet. Recovery only available last nite. Guess they need to refine it to be able to flash using the recovery available. I suppose they were based on Chainfire CWM when they develop it. Brood dont even have a phone to test it!!

No such issues at all

Sorry, I still dont see it ;
Please give me a link to test it again

That is quite high. Mine last night over 5 hours with 3g on drop 4% n I still consider satisfactory only. On note2 example drop most 2 % over 7 hours while is close to zero in xperia z over 7 hours . I stop using phone when battery level was 85%

Highly recommend xperia z if you want LTE now
Is a darn good phone vs S3. Only major issue is its weaker poorer audio quality but can be improve with root n mod applied

I will instead sell off my S4 n keep the Note2

It is purely my personal preference
I always prefer a bigger size display phone as my main phone. I have bought and tested xperia Z ( 5 inch), HTC One ( 4.7 inch) and now the S4 ( 5 inch). None of these 3 can ever matcgh the satisfaction of using a 5.5 inch. I have even bought the Pantech Vega No6 wich comes with a full HD 5.9 inch display ( should be receiving it tomorrow)

The only obvious advantage of the S4 over the Note 2 is is its amazing full HD display - Samsung's finest to date. Even though is still pentile based it does not in any way loses out to HTC One
As I am not a gamer, the better and more powerful processor is insignificant to me

One major disappointment of the S4 is its obviously poorer audio quality through its phone speakers vs Note2. The other minor issues ( to me ) is still the unrefined TW additional software stuffs ( I have posted before my comments on these) and the available only 8.8 gb internal storage ( vs 11 gb of Note 2, S3) to user