Not even remotely.
You were making the argument that a vampire's charm is weaker than domination spells. A player could say, "fine I accept your argument" and then argue that substituting vampire's charm for one of the dominate spells available to players wouldn't upset game balance. On the contrary, the players would be using a custom spell that is "inferior" to the spells in the RAW. It's a classic argument/negotiation error. I.e., don't be surprised when B'rer Rabbit wants to go into the Brier Patch, or when you find out that you really did sell Jack magic beans.
I don't see the improvement. This spell as you've revised it looks like it's designed to be used to make your enemies toss themselves into danger on your behalf (until they make their save, anyway). Charm Person, as designed, isn't that spell. It's not meant to be.
Funny, it worked that way in BECMI. Rules Cyclopedia, Charm Person:
[...]the victim will believe that the spellcaster is its "best friend," and will try to defend the spellcaster against any threat, whether real or imagined.
the spellcaster may give orders to the victim. These orders should sound like suggestions, as if "just between friends." The charmed victim will usually obey, but the victim may resist orders that are contrary to to the victim's nature (alignment and habits) - he doesn't need to roll anything to resist. A victim will refuse to obey if ordered to kill itself.
And in AD&D. Magic-User version is as the spell, Charm Person or Mammal:
The creature will then regard the druid who cast the spell as a trusted friend and ally to be heeded and protected. The spell does not enable the druid to control the charmed creature as if it were an automaton, but any word or action of the druid will be viewed in its most favorable way. Thus, a charmed creature would not obey a suicide command, but might believe the druid if assured that the only chance to save the druid's life is if the creature holds back an onrushing red dragon for "just a round or two."
And in AD&D 2nd Edition. Charm Person:
If the spell recipient fails his saving throw, he regards the caster as a trusted friend and ally to be heeded and protected. The spell does not enable the caster to control the charmed creature as if it were an automaton, but any word or action of the caster is viewed the most favorable way. Thus, a charmed person would not obey a suicide command, but he might believe the caster if assured that the only chance to save the caster's life is for the person to hold back an onrushing red dragon for "just a round or two."
And in D&D 3rd Edition. Charm Person:
[...]This charm makes a humanoid creature regard you as its trusted friend and ally (treat the target’s attitude as friendly
The spell does not enable you to control the charmed person as if it were an automaton, but it perceives your words and actions in the most favorable way. You can try to give the subject orders, but you must win an opposed Charisma check to convince it to do anything it wouldn’t ordinarily do. (Retries are not allowed.) An affected creature never obeys suicidal or obviously harmful orders, but a charmed fighter, for example, might believe you if you assured him that the only chance to save your life is for him to hold back an onrushing red dragon for “just a few seconds.”
***
Dominate Person is that spell, which is why it's Concentration and lets you dictate actions and keeps going when the victim is hurt (until they make their save, anyway).
A vampire's charm serves a different function than each of those effects, as well.
Yeah and I'm saying I'd rather have those "different" effects; I'd rather have the vampire's charm effects than Charm Person or Dominate Person.
Am I missing something, or did the one extra word you add not actually make any real difference in how these spells work?
No, I pasted the wrong text in the first quote. The passage should read:
Replace the following text in the spell description:
Dominate Beast, Dominate Monster, Dominate Person:
Each time the target takes damage, it makes a new Wisdom saving throw against the spell. If the saving throw succeeds, the spell ends.
With the new text:
Each time the target takes damage from you or your companions, or as a direct consequence of your or their actions, it makes a new Wisdom saving throw against the spell. If the saving throw succeeds, the spell ends.
***
Monsters aren't player characters. They don't and shouldn't need to obey the same rules or have the restrictions. They can have one-shot kill powers (like the banshee) or potent communities or immortality.
They don't need to be balanced for play over 20 levels fighting 1-6 encounters. They just need to exist for 2-10 rounds of combat and then go away.
Players shouldn't have nerfed Charm/Dominate spells, if Monsters have Charm/Dominate that read like the Charms in BECMI/1e/2e/3e. Vampire's charm is like an at-will 15th level spell, going by the way the Charm/Dominate spells available to players are written.
I hear that you're disgruntled with charm/dominate abilities in 5e, but it might be helpful to be precise about what you actually want them to do. What's the goal here?
What I accomplished with the rewrites.
What's the problem?
To me at least, they're two abilities that serve different functions in the game. I don't expect player/monster symmetry.
Player/monster symmetry is irrelevant. I don't want the Charm/Dominate spells available to players to completely suck compared to the vampire's charm, especially when the latter is an at-will ability that lasts 24 hours and doesn't require concentration. Never seen anything in the lit to support the idea that vampire's charm rules while the enchantress' charm drools.
I'd rather see classic spells bumped up in level until they're balanced than see their descriptions nerfed.
Eh, the uber-powerful charm spells of this edition are the Suggestion spells. Sure, you only get one command, but that command can be anything short of suicide if you word it well, the duration is great, and Mass Suggestion doesn't even use concentration. i wouldn't trade them for Vampire Charm.
Yes, suggestion, geas, etc., are all much better than the charm/dominate spells.