They both support Linux. Some (not all) EZbook users have had trouble with the touchpad not working under Linux. This is a problem that various notebooks have not just Jumper. There are updated drivers in the works for this though depending on which touchpad yours has (they swap parts a lot when building them). I would go with the Lapbook SE. It’s quite a bit faster with the Celeron N4100 and so far as I have heard no problems with the touchpad. You can somewhat compensate for the 2GB less ram (4GB vs 6GB in the EZbook) by installing a slimmer/lighter Linux distribution.
The default LinuxMint Cinnamon 19 that Chris tested, is not the lightest/smallest one. Better ones for a 4GB machine would be IMO…
LinuxMint Xfce I think this will install the Grub boot manager and work fine for dual-booting with Windows
Manjaro Xfce 18 (*may*, not sure, require extra install/setup of the rEFInd boot manager for getting dual-boot with Windows working)
It’s also helpful to use a lighter-weight browser like the Falkon browser.
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