If its at your house I would look into getting a more powerful router because my turbo is bounds and leaps better than my s4. At work in areas where I used to get no WiFi signal to just enough to show up as a network I now have two bars of wifi signal in those locations.
Same house, same router, same weather, same time, same place, both phones side by side, dBm monitor software running, the DT averages 5dBm worse than the S4. A more gross test is to open youtube and click play on same vid at same instant, the Turbo stops to buffer and lags behind the S4 significantly.
I do think the Youtube app on the Turbo is having issues since it'll stutter a bit within three feet of my router, but it's still a connection issue. Another obvious test is the S4 shows half a dozen or more nearby but very weak wifi AP's, the Turbo shows mine and one other, occasionally seeing a 3rd. Similar behavior from my Nexus 7 tablet, it's not as bad as the Turbo, but not as good as the S4.
It's not dramatic but the S4 will have functional wifi in a fringe area (my shop, my backyard) when the Turbo does not. WiFi like any other radio signal is inconsistent and variable and it takes some serious study and comparison to make definitive observations. The stock signal bar icon is next to useless on any of them for anything but very general signal strength as well.
Moto contacted me wanting some log files to see what the deal is and I'll help them out if I can, but I suspect 5dBm give or take isn't enough for them to worry about, and it's not till you are in a fringe area when every bit counts. If I didn't hang out in my shop or sit in my backyard where I know the S4 works I might not have noticed it so quickly. I have a pretty decent dual band/antenna Asus router just so I could have useable wifi back there.
It's not the end of the world, but it's there.