The numbers you provide (AX 3000 and AC 1900) are aggregate capacity ratings from the manufactures in an attempt to allow comparison of router throughput capacities from different manufacturers. More of a marketing label. In this case, apples and oranges when you consider the additional Wi-Fi band of the AX device. You are going to need to compare actual reviews of specific model numbers of the Wi-Fi routers.
In general, AX devices are a newer fresher design compared to AC devices. Also AX devices will most likely be supported by the manufacturer farther into the future than AC devices.
I’m mainly looking for best range at 5Ghz speeds (it’s a big house), especially for gaming and streaming (ethernet not applicable).
It may not be possible to get a single router to fill the space. Wifi strengths are limited by law, and most brands are likely to have the same signal strengths. After all, the wifi chips come from a small bunch of third party suppliers.
You may want to look into something like an Orbi Mesh system, wirth a router and as many satellites as you see fit.
