The main technical difference between how Termux and KBOX runs packages is that is that KBOX uses libfakechroot for running binaries under a fake chroot environment, while Termux runs without a chroot, having instead patched the packages to live under the file system hierarchy enforced by Android.
Besides that, the ambition is that Termux should give a more "out of the box" user friendly experience directly after installation to encourage newcomers to the world of terminals :).
Since Termux requires Lollipop or later, and TerminalIDE only works on Android versions prior to lollipop, TerminalIDE could be an alternative for devices running older Android versions.
Thanks for trying it out - let me know if you have any suggestions for improving the app!