I just wanted to share this with the community. I make absolutely no guarantees on how well this will work for you, but this is what worked for me and I hope that it might be able to help you as well!
Backlog: I picked up my GS4 about 3-4 weeks ago and had been experience the typical lag and stuttering issues during page switches, app switches, and quite a bit of noticeable lag in my games (Hill Climb most notably). I scoured the internet looking for ways to alleviate the problem but was never able to completely get rid of the lag or stutters that this device seems to suffer from. One of the most frustrating parts about reading the other fixes online all had to do with disabling all of the cool effects and animations a phone of this caliber should be able to slice right through. The fix that I found, and works for me, doesn't make you sacrifice the phones awesomeness for stutter free operation. After making a few tweaks in the Developer Options as well as changing or disabling some effects, I can now say that my phone is completely lag and stutter free. I haven't had an animation stutter since making these changes nor have I had a single bit of lag in any of my games. Read on for how my phone is setup and how you may be able to fix yours as well!
MY SETUP
Apps:
Settings:
-[Optional] Disable Lock Screen "Unlock Effect" - This really will have no bearing on the lag/stutter problem but I find that since it does take additional time to load these effects when you wake up your phone I prefer the responsiveness of the original swipe unlock effect. (Settings > My Device > Lock Screen > Unlock effect)
-[Optional] Disable S Voice "Open via the home key" Option - This will greatly speed up the responsiveness of the Home button if you do not use S Voice or make use of it's double tap feature. (S Voice > Menu > Settings)
Developer Options:
-Animation Scales: 0.5x (This step is about personal preference, honestly. Decreasing this setting from 1x to .5x will make the animations take half as long as they do by default which will make your device feel much more responsive, instead of waiting around for the nifty animations to dazzle you.)
-Disable hardware overlays: Check
-Force GPU rendering: Check
-Enable 4x MSAA: Check (This option really will have no bearing on lag/stutter issues, in fact if it has any impact at all it would be in games which would potentially slow them down or cause them to lag as forcing anti-aliasing is going to increase GPU load. However with this enabled I have seen no such sign of lag in my gaming and it only serves to make your games look better. Go ahead and enable it.)
-Limit background processes: 4 processes at most (This will help keep your RAM from getting tied up by applications that you are no longer using, etc rather than sitting idle hogging up memory you could be using for other things)
I am very anxious to hear if doing these things helps anyone else out. I can say with certainty that this combination has breathed new life in to my stuttery S4. Please post your results and let me know if this works for you as well. CHEERS!!!

Backlog: I picked up my GS4 about 3-4 weeks ago and had been experience the typical lag and stuttering issues during page switches, app switches, and quite a bit of noticeable lag in my games (Hill Climb most notably). I scoured the internet looking for ways to alleviate the problem but was never able to completely get rid of the lag or stutters that this device seems to suffer from. One of the most frustrating parts about reading the other fixes online all had to do with disabling all of the cool effects and animations a phone of this caliber should be able to slice right through. The fix that I found, and works for me, doesn't make you sacrifice the phones awesomeness for stutter free operation. After making a few tweaks in the Developer Options as well as changing or disabling some effects, I can now say that my phone is completely lag and stutter free. I haven't had an animation stutter since making these changes nor have I had a single bit of lag in any of my games. Read on for how my phone is setup and how you may be able to fix yours as well!
MY SETUP
Apps:
- Nova Launcher Prime (Much better code optimization than TouchWiz, it makes for a more enjoyable user experience)
- Clean Master (use this app to keep your device cache cleaned up, the less amount of data the phone has to work through the better)

Settings:
-[Optional] Disable Lock Screen "Unlock Effect" - This really will have no bearing on the lag/stutter problem but I find that since it does take additional time to load these effects when you wake up your phone I prefer the responsiveness of the original swipe unlock effect. (Settings > My Device > Lock Screen > Unlock effect)

-[Optional] Disable S Voice "Open via the home key" Option - This will greatly speed up the responsiveness of the Home button if you do not use S Voice or make use of it's double tap feature. (S Voice > Menu > Settings)
Developer Options:
-Animation Scales: 0.5x (This step is about personal preference, honestly. Decreasing this setting from 1x to .5x will make the animations take half as long as they do by default which will make your device feel much more responsive, instead of waiting around for the nifty animations to dazzle you.)
-Disable hardware overlays: Check
-Force GPU rendering: Check
-Enable 4x MSAA: Check (This option really will have no bearing on lag/stutter issues, in fact if it has any impact at all it would be in games which would potentially slow them down or cause them to lag as forcing anti-aliasing is going to increase GPU load. However with this enabled I have seen no such sign of lag in my gaming and it only serves to make your games look better. Go ahead and enable it.)

-Limit background processes: 4 processes at most (This will help keep your RAM from getting tied up by applications that you are no longer using, etc rather than sitting idle hogging up memory you could be using for other things)

I am very anxious to hear if doing these things helps anyone else out. I can say with certainty that this combination has breathed new life in to my stuttery S4. Please post your results and let me know if this works for you as well. CHEERS!!!