S3 works well side by side with iPhone. There could be reception issues on the iPhone or a an issue with what's displayed on the screen at least?
Because try holding Ur phone like Ur texting (so holding it with both hands on the sides), I usually lose a couple bars on 3G or if I m on LTE, I drop down to 3G.
I went outside my house, 4 bars on LTE, walk back in: 2 bars of LTE at certain sweet spots and it keeps dropping. Exact same at my university which is in the middle of Edmonton. LTE drops the second I get beneath anything. My LTE dropped when I sat under a tree. Maybe it's just showing 3G when it might be connected to LTE? Or this might have a reception issue.