It's mainly the release model.
Kubuntu is Ubuntu. So, two major updates a year, where the state is basically "frozen" in between. This gives everyone time to fix bugs, giving you a more stable experience.
Neon is rolling release on everything regarding KDE, but has a very stable base OS. Advantage: newest and hottest KDE stuff, but it maybe has some rough edges and doesn't provide you with the newest kernel, which usually isn't a big deal, but you might miss out on something.
Is there a reason why you want something Ubuntu based?
You also have a few other options:
- Debian: older (still has KDE 5.27), but very stable and tested
- Fedora KDE: similar to Kubuntu, but more vanilla and less shitty in my personal opinion (Snaps, etc.)
- EndeavourOS: Arch based, beautiful customisations applied OOTB, sane defaults if you like Arch
- Fedora Atomic KDE (Kinoite) or Aurora: the newest image based (immutable) variant. It's what I use and would recommend. Very reliable!