Ubuntu Mini Remix vs Ubuntu Core

The Ubuntu Core is a minimal rootfs, thus you'll miss the booting components, you should take an official Ubuntu CD, remove the squashfs and replace it with the Ubuntu Core, plus you'll have to add a user (as written https://wiki.ubuntu.com/Core Ubuntu Core doesn't have one).

Ubuntu Mini Remix has the booting components, and something like the Ubuntu Core rootfs, plus the standard ubuntu user preconfigured.

Plus, on the Ubuntu Core page it's not stated which are the included packages. For Ubuntu Mini Remix the packages list is here: https://answers.launchpad.net/ubuntu-mini-remix/+faq/33 and you'll be sure to have the minimal set of packages to create a full featured Ubuntu derivative.