There is a lot of misinformation on the role of Cha even for Enchanters/Bards. Some people swear that Cha only effects initial resist for Charm, and not Charm duration.
The
most common view is that every 6 seconds during a charm, mobs roll a check based on some formula against, in order (1) the level difference vs. the enchanter, (2) the MR of the mob, and (3) the Enchanters Charisma. So basically, if the mob loses the level distance roll, it stays charmed. If the mob wins the level distance roll, then it rolls an MR roll. Only if the mob wins both the level difference and the MR roll does it even bother checking Cha on an enchanter, which is why everyone says the most important things in charm duration are level difference and MR.
If this is the correct understanding of how enchanter charm works (correct me if I'm wrong), then what happens for Druids and Necros is that there is no third roll for a charima check. The question then becomes whether the rest of their Charm roll formula (the way the level and MR checks are calculated) are somehow more favorable as a result, or whether druid and necro charms with similar MR levels should just hold less long due to the lack of a charisma roll.
Then, only having answered those questions, can we get back to the framing that Daldaen put: do non-charm classes utilize the enchanter/bard formula (with a cha check), or the druid/necro formula (with no cha check).
Assuming no dev input, the real answer has to be parsing a lot with puppet strings, which given the need to run like 100 samples at different cha levels for three classes (enchanter, necro or druid, non-charm class) is unlikely to happen.