The biggest issues with I-80 and I-70 are elevation.
I-70 crosses the Colorado rockies at over 10,000 ft.
I-80 across Wyoming doesn't go as high, but is still over 8,000 ft across much of Wyoming, on a high plain that can see high winds, and can add to the challenges if there is snow. I-40 by comparison is generally in the 5000-7000 ft range across NM and AZ.
Both could be perfectly fine, those factors can increase the risk of bad weather though. Taking I-80/I-76/I-70 through Nebraska and Colorado is actually slightly shorter than the route I recommended, and it's also a beautiful drive in good weather. But noting your concerns about snow, the difference is small enough that I think you'd find the I-40 based route a little easier, if the weather conditions are equal.