At that price point ($300 max), you won't get G-Sync monitor. Also, Freesync is used with Radeon GPUs while what you have is Nvidia GPU. Only thing that you can do, is to enable Nvidia Adaptive Vsync under Nvidia Control Panel settings. (I've done that with my Nvidia GPU and Freesync monitor.)
What you've linked are 2x 27", 1080p monitors with 75Hz refresh rate, TN panel and 1ms response time. Between the two, i'd go with Asus monitor since it's known and trusted brand. Iiyama is unknown brand to me and i, personally, wouldn't pick that one. Monitor specs as well,
Asus:
https://www.asus.com/Monitors/VG275Q/
Iiyama:
https://iiyama.com/gb_en/products/g-master-gb2730hsu-b1/
With $300 budget, i'd go with 27", 1080p, 144Hz, VA panel and curved screen monitor instead, e.g:
MSI Optix G27C2, amazon:
https://www.amazon.com/MSI-Non-Glare-Refresh-FreeSync-G27C2/dp/B074G96MPM
AOC C27G1, amazon:
https://www.amazon.com/AOC-C27G1-Frameless-DisplayPort-Adjustable/dp/B07GD5XG5G
Acer ED273 Abidpx, amazon:
https://www.amazon.com/Acer-Monitor-Refresh-Compatible-Display/dp/B075KFPJ5C
Besides double the refresh rate (144Hz vs 75Hz), you'd also get much better color accuracy with VA panel than TN panel. Also, VA panel contrast ratio is the best of all panel types (TN and IPS being the other two) where VA panel contrast ratio is easily 3000:1, compared to the max 1000:1 of TN and IPS panels. Oh, Acer monitor has 4ms response time while MSI and AOC monitors have 1ms response time, just like on those two TN panel monitors you picked. Since all 3x VA panel monitors have curved screen, they also add quite a bit to the immersion of gaming experience.
I have
MSI Optix MAG241CR monitor in use (24", 1080p, 144Hz, VA panel, 1ms, curved screen) and i can say from my personal experience that VA panel monitor is a lot better than any of the TN panel monitors, both for gaming and casual use.
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