@alexxs88 - when you say incredibly slow, is it in the double digit slow, like 20Mbps?   I have a similar set up as you and am using the S4 in AP mode as well.   See my other post as I've been able to fix my issue by reading the logs and seeing a message that appeared to be really off.  

@fpgirard I mentioned in the message. It drops to 100Kbps or so. I'll check your thread. Thanks!

@fpgirard can you please tell me where I could find the system logs and how you've resolved your exception?

@alexxs88 - hi - like the TP-link moderator said, go to the web interface, select advanced, and you'll see the system log entry in the left column. 

I went ahead and downloaded the entire log to my Mac and used my favorite editor (Sublime) to see what was going on,  gazillion entries like the one I posted were logged for a single device.   See if there's a device on your network that is forcing the main router to use all of its resources logging.  That was the problem for me.

Good luck - keep me posted!