In terms of raw download speeds, you typically won’t see a massive difference between a USB 2.0 and USB 3.0 adapter. The max throughput of USB 2.0 is considerably higher than that of the average Wi-Fi connection, and USB 3.0 even more so. However, that doesn’t mean you shouldn’t get a 3.0 adapter whenever possible.
First and foremost, a 3.0 adapter will be able to keep up with particularly high-performance Wi-Fi networks. Particularly, connection speeds of over 100 Mbps, with routers using 802.11ac and broadcasting at 5 GHz.
But more importantly– even for slower networks– latency. USB 3.0 has much lower latency than USB 2.0, and latency is especially important for gaming. High latency results in a laggier, less responsive online gaming experience. Using Wi-Fi at all already increases latency, but using a USB 2.0 adapter on top of that can result in an unplayable experience for gamers.
If you’re going to game on Wi-Fi, a USB 3.0 adapter is a necessity, not an option.