I can tell you my experience as I owned a iPhone 5 since release to about May and an S4 from May onwards
The long of the short of it: Wouldn't even entertain the idea of going back to an iPhone 5/5S or anything that doesn't rock a 5 inch display..
The S4 is a great piece of phone. People are always complaining that the build quality coming from an iPhone will be diminished, and it is correct since the S4 is polycarbonate. But when I held my S4 in the ATT store as my service was being switched over, I really couldn't complain. I really love the way my S4 feels. The phone itself is brilliant plauged by bloated software. I run a custom rom Called GoldenEye ROM which essentially takes the TouchWiz Software and completely debloats it. I remember the night when I booted up the ROM and it made my phone feel completely brand new. Even stock the phone is great but my GOD does the phone run smoother and considerably longer than stock or my iPhone.
Regarding the battery life, the stock S4 does indeed have more battery life and it shows in real world usage. I can say my ROM'd S4 gets almost 40-50% better battery life than my iPhone 5 at max brightness and power saving off with 4G. Stock S4 is still looking at a healthy 20-30% The reason is although the S4 rocks a much bigger screen, it uses a much more efficient AMOLED display, and if you pit an iPhone 5 against the S4, the iPhone 5's screen is considerably brighter HOWEVER that doesn't mean that the S4s screen lacks. Its size more than makes up for the brightness, and trust me on this, its still more than enough. Regarding the screen, samsung gets its awesome critiques from its screen due to the fact that it is designed to oversaturate colors making them more vibrant and such. Coming from an iPhone 5 you could easily tell. The first couple days, pictures on Facebook looked competely fake. colors were too bright, the darks were too dark, it just wasn't realistic. I have now gotten used to it and I can't even tell but I will warn you that the screen is NOT mean't to be accurate, its mean't to accentuate colors. The screen is still absolutely gorgous, and even today I still sometimes stare at it admiring my HD wallpaper because it looks so **** good.
Regarding speed vs the iPhone 5. The S4 might rock more than twice the cores than an iPhone but I still noticed that on stock the S4 was a tad bit slower than my iPhone 5 starting up apps. Is it a dealbreaker? NOT BY ANY MEANS. The phone itself is so good that you will notice it, but quickly dismiss it. Now if you run a custom debloated ROM, then the story is much different. The phone will either be THE SMALLLLLLLLLLLLLLEST increment slower than an iPhone but will 90% be just as fast and in some instances faster.
Music wise, the S4 is a mile behind the iPhone 5 in terms of SQ. If you have gotten used to your iPhone 5's musical SQ, you're going to hate the S4. Unless you get it rooted and install Viper4Audio. Then.....then you will hear things in your music that you never heard on your iPhone 5. If you DEPEND on SQ from your S4, then I would either go with an HTC One, or stay with the iPhone 5. If you want to root your phone, then BY GOD PLEASE get an S4. Once this phone is ROM'd and ViperAudio'd, there is not a SINGLE thing you would want from your iPhone 5. Literally the only thing you could want is the fluidity of iOS, but even ROM's make this problem go 95% away.
The camera. Best camera I have ever used on a smartphone. Hell, its not saying much, but its the best camera I've ever used. The detail is astonishing and the colors pop (on your phone. good for when you want to impress friends) but once you upload it onto a computer and see the actual colors, its a little less astonishing, but still good none the less
I love my S4. I don't even THINK about iPhones anymore. What I would do is go to your local wireless provider and try the phone out as well as other phones
Some phones I would be on the lookout for
LG G2
Google Nexus 5
HTC One
Hope this answered some of your questions //content.invisioncic.com/y282845/emoticons/smile.gif.1ebc41e1811405b213edfc4622c41e27.gif