Which one will offer me a better Wi-Fi connection and how big would the difference be?
Also, just a follow-up question:
What kind of router would I need to optimize either of these Wi-Fi adapters?
The motherboard WIFI includes an external antenna. Getting the antennas out from behind the case can have a big improvement.
There are many variables in WIFI performance. How far away, how many walls, what kind of walls, interference from other WIFI...
The best performance you can get is not using WIFI. Ethernet cable is best, then if you have coax, MoCA, then powerline networking and finally WIFI.