Lenovo's ThinkPad line has a sterling reputation. Among the best in terms of quality, service, repairability, and Linux support.

As for the largely consumer-grade options of ASUS and Lenovo's consumer-grade IdeaPads, they're rather similar in reputation and quality. Not exceptional, but they're both perfectly fine options as long as you avoid the budget laptop segment (plastic chassis, broken hinges, etc.)

Any difference in privacy would come down to the pre-installed software, which is irrelevant if you plan on using Linux. If you will be using Windows, it's always better to install your own fresh copy to purge any potential spyware and bloatware installed by the manufacturer. The activation key for whichever edition of Windows it comes with is embedded in the BIOS, so it'll activate automatically after a fresh reinstall.