Honestly I wouldn't get either of these laptops. Their 15.6" 1366x768 TN displays don't let you fit much onscreen, and have very poor contrast + colors + viewing angles. The display is one of the most central components to a laptop, and differences between different displays tend to have a pretty big impact on how nice the computer is to use. I think you're far better off worrying about what display you get versus what processor the laptop has, as most of today's processors are plenty fast enough to do most normal things someone would do with a computer, whereas these lower-end 1366x768 TN displays are actually rather bad.
Can you go $399? If so, I would recommend the Dell i5559 through the current Microsoft Store deal. This specific listing:
https
/www.microsoftstore.com/store/msusa/en_US/pdp/Dell-Inspiron-15-i5559-Signature-Edition-Laptop/productID.333089700
Has a significantly better 15.6" 1920x1080 IPS display. The 1920x1080 resolution increases the amount of windows you can fit onscreen, and the contrast + colors + viewing angles are all much better on this display too.
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Alternatively there is the Lenovo Thinkpad E570. Also available with a 1920x1080 IPS display, but trades touchscreen, i5, and disk space for better build quality and a (presumably) nicer keyboard: https

/www.reddit.com/r/SuggestALaptop/comments/5fewg9/15in_usa_500ish_looking_for_a_laptop_for_my_mom/dajs844/
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Alternatively again, grab either the HP 15t or 15z laptop you're looking at, and pick the 1920x1080 IPS display upgrade on the configuration page. Pick this upgrade first before you decide what other upgrades you might be able to fit in your budget, as the screen will make more of a difference than them all.
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Finally, if you can't go over $329, get this Acer:
https
/www.amazon.com/Acer-Aspire-i3-7100U-Windows-E5-575-33BM/dp/B01K1IO3QW
The display is not IPS so the quality isn't great, but you still get the 1920x1080 resolution versus 1366x768, so you're not so limited as to how much you can fit on your screen.