I am wondering which would be a better phone to buy Samsung Galaxy S3 vs Asus Zenfone 5?

Most important is call quality.

Rear Camera

etc

Difficult question, I considered both these but got the z5. Part of my decision was based on my gf's galaxy s3. It was great all round when she got it but after a few months she started having major battery issues with it. It was also super fast in the beginning but with all the Samsung UI updates it was really lagging after some time. The new s3 is running a newer version of Android so don't know if that improves it, but in any event I'm not so keen on the Samsung touchwiz thing and wanted more of a plain android set up on the phone.

My wife has a zenfone 5 for a couple of months now and after my Samsung note 2 crapped up this week, I bought me one as well. Very happy with it, snappier as the note 2,no more Samsung bloatware and a third of the price.

I have a Zenfone 5 and unless your concerned about face, I don't know why you would bye any other phone, except for maybe the 6, the larger screen is quite nice.

I would also look at the Benq F5. LTE and 3g. Snapdragon 400 processor etc.. http://www.lazada.co.th/benq-f5-black-333274.html