From what I have been told, 3rd party launchers, etc. make a lot of difference. I just can't justify that much money, and worry about lag, because I'm sure that I wouldn't be one of the lucky ones.
The problem here is that you have not really used the S4. So, not to be mean, but you can't begin to discuss lag on that device. Again, not to be insulting, but your conclusions seem to be totally based on what some friends told you.
I use IOS 7 and My S4 every day. Both have their annoyances. I have zero lag (zero, as in none, zip, zilch) with either my apple or Android devices. I did take the time to optimize my S4, which is probably why I am "lucky". In the world of tech, I have found that luck usually translates to be willing to take the time to actually learn how to use something.
For me, I like my IOS devices for their elegance, stability, and integration, I think IOS 7 is really pretty and likedit from the moment I upgraded. I am actually typing this post using it!
But, I find the S4 and my Nexus 7 a lot more fun to play with and I have found it much easier to overcome limitations on Android due to the customization.
Both systems also have killer features that I badly miss. I miss iMessage on my S4, and I could barely text without swype on the iPhone. And, the integration with google apps is a bit nicer on Android.
I would not say one OS is clearly superior to the other, but I will stay with my s4.