I have an Intel wireless device and a TP-Link TL-WN722N and the Intel works much better. I am going to recommend some changes to you and I suspect that, if you undertake all of them, the internal Intel device will work very well.
First, turn off power saving in Network Manager. From the terminal:
sudo sed -i 's/3/2/' /etc/NetworkManager/conf.d/*
Next, I recommend another change to Network Manager.
sudo nano /etc/NetworkManager/NetworkManager.conf
Edit the file so that it now reads:
After making any needed changes, save the file (Ctrl+o followed by Enter) and exit nano (Ctrl+x).
Reboot the computer.
Next, as has been noted, many Linux drivers, including ath9k_htc and including iwlwifi hate hate hate TKIP.
Please check the settings in the router. WPA2-AES is preferred; not any WPA and WPA2 mixed mode and certainly not TKIP. Second, if your router is capable of N speeds, you may have better connectivity with a channel width of 20 MHz in the 2.4 GHz band instead of automatic 20/40 MHz, although it is likely to affect N speeds. I also have better luck with a fixed channel, either 1, 6 or 11, rather than automatic channel selection. Also, be certain the router is not set to use N speeds only; auto B, G and N is preferred. After making these changes, reboot the router.
After all these changes, is there any improvement?