Distance will be the same because both are nano receivers, external antenna's do help with range. However, bandwidth will be double at the same reception level because the 300mbps unit most likely uses dual internal antenna's. So say you have a 2 out of 5 bars of signal strength and that's good for 20mbps with 1 antenna. With two antenna's you'll get 40mbps of bandwidth. Depending on your application, you may not need the extra bandwidth and the slightly smaller unit is better.
If this is for a laptop who's receiver died. I'd upgrade it to a newer wireless AC unit. Normally this is very easy to do with most laptops. Just flip it over, unscrew the access cover, and plop the new one in. Laptops have the antenna's alongside the lcd screen, so they get great reception.
If this is for something like a raspberry PI. I'd recommend a wireless media bridge. Some routers can be reconfigured as a wireless bridge/ wifi access point if you happen to have an old spare router laying around. Otherwise you can just buy a wireless adapter that bridges with an ethernet cord to the pi, but has a full size antenna and amplifier. If your main router is wirelessAC and you are using this for a raspberry PI, I'd recommend you buy an ASUS wirelessAC router and reconfigure it as a wifi bridge. The AC51U is the cheapest router they have with bridge mode, and it works very well. I use a more expensive 4 antenna model for a wifi bridge and it actually gives me sustained gigabit speeds.
https://www.amazon.com/Dual-Band-AC...+wireless+AC&qid=1553692727&s=gateway&sr=8-19
If you're still having trouble trying to get wifi to the other side of your apartment or house, I'd recommend MOCA or powerline ethernet. Don't use wifi repeaters, from experience in knowing people that bought them (ignoring my advice), they usually don't give very good bandwidth. My brother bought a wifi repeater and it could only muster a sustained 10mbps when placed halfway to the other side of his house. I made him get a powerline extender linked here, and now he can sustain over 100mbps of bandwidth.
https://www.amazon.com/NETGEAR-Powe...line+ethernet&qid=1553693045&s=gateway&sr=8-7