Me too have Samsung Galaxy S4 but it is a pretty old phone now and as the new year is coming there will be a lot of offers around to the corner to flood the market.
LG G2 Flex would be a nice phone that I would suggest you and I am also considering that phone as I have tried it and runs pretty good.
But if you want to go for some other then Nexus 5 is also there and this phone also offers everything that the S3 users would like to have in there next phone.
So my pick is between LG G2 Flex and Nexus 5.
You can also check the specifications of both of these before going to any of these.
LG G2 Flex - http://www.yogadz.com/phones/lg-g-flex-specifications/
LG Nexus 5 - http://www.yogadz.com/lg-nexus-5-specifications/
I want a phone with these specs :
2 GB ram minimum
2500 ma battery minimum
8 megapixel minimum
Full hd display
1.7 Ghz min
4-5.5 inches screen
Note : i actually have the gs3