My $0.02.
I use the Odroid-XU4 with eMMC for several different mini-PC needs, including Linux & Windows. (they're great for KIOSKs, especially when you match them with a touchscreen and a 3D printed enclosure.)
When considering just the pure reliability aspect of eMMC against MLC/SLC flash, or against HDD, keep in mind for the mini-pc discussion it should be about MicroSD -vs- eMMC. In that discussion there's no debate, MicroSDs go corrupt 'all of the time' for 'no random reason', where eMMCs are rock solid.
The performance aspect is another great eMMC benefit. 600MBs sustained read/write is insane compared to MicroSD. Even if you use USB3.0 to a proper SSD, which is the only valid mini-pc option for direct connected persistent storage, eMMC is pretty on par. 'good enough'
If you're having issues booting from it, i'd double check the BIOS/firmware capability of your particular mini-pc. It's not always easy
There's 'options' like, using MicroSD only for your Boot Loader area (not the best option, but totally viable)
In a lot of other cases, you have to install your OS to MicroSD 1st. (it's a big pain).
Then take your MicroSD and eMMC devices on a linux host and use DD to 'mirror' them.
After you boot from eMMC via this cheat, you can patch going forward, it's just a 'new OS setup' thing for the bootloader region.
Google-foo for Odroid installation instructions for how to migrate Linux from MicroSD to eMMC.
Those instructions should work 'relatively' the same for any OS you want to install on your mini-pc.
(assuming you have a linux box or linux USB thumb booter, you can use to do the MicroSD to eMMC cloning part)