Susan, the Asus obviously costs a bit more than the Acer. (I am comparing two that both have 4GB of RAM and 64GB flash memory for the OS;- Asus is $462.90, Acer is $391.53.) The Asus does have a much faster CPU than the Acer so it would be a little more responsive. And it's a "2-in-1" meaning you can flip the Asus over and flatten the keyboard, to make it kind of like a thick tablet. The Acer is just a standard laptop-style, not a tablet. So, you are getting more for the extra money if you buy the Asus.
The Acer does claim a 12 hour battery life though vs. "only" 10 hours with the Asus. I doubt you'll really know the difference - maybe on a long international flight, the extra two hours might matter. (In reality, both are probably less than advertised.)
One thing to watch out for with Chromebooks is that they have a specific end-of-life date for support, after which they cannot be upgraded (but you can keep using them). By contrast, Windows laptops do not generally have that problem; you could still install a free upgrade to Windows 10 of an old Windows 7 computer you bought ten years ago. (though it might be kind of slow with WIndows 10 - but at least you could.) Chromebooks are supported for about 6.5 years and then that's it - no more security updates, etc. Time to buy a new one. I don't know when each of these sees its end of support; Google is supposedly making that more clear now than they used to. More info here:
Chromebooks do support Android apps now, which is pretty cool. (Both Chromebooks and Android come from Google.)