In terms of points cost (for Matched play) the two entries are identically costed: the individual model and every option costs the same, whether bought from the Heretic Astartes or Chaos Daemons army lists. However the Power Rating (used for Narrative play) differs: 10 for Heretic Astartes and 11 for Chaos Daemons. That's an odd inconsistency; I'd have thought it more likely to have different points for the same Power Rating rather than the other way around. But note that the Power Rating represents the average expected load-out (according to the designers) so perhaps they have data that shows the Chaos Daemons flavour of Prince is usually given more expensive options? Anyhow, there are mechanical differences too, and that's more interesting to me.
In the following list, I've coloured lines in green that favour the Heretic Astartes (HA) Daemon Prince and red for the Chaos Daemons (CD) Daemon Prince. This is just the list of differences; all other features (including weapon profiles) are identical for the two entries.
- Wounds: 8 for HA, 10 for CD. That feels like a major differentiator!
- Leadership: 10 for HA, 9 for CD. Not hugely significant. The standard Morale test won't ever affect the Daemon Prince since it's a single model, so this is going to matter only depending on what other abilities are in play in the opposing army.
- Death to the False Emperor: HA only. If targetting an Imperium unit (and there's a lot of them) in the Fight phase, for every hit roll of 6+ you immediately get another attack against the same unit with the same weapon (that doesn't generate any further attacks).
- Daemonic Ritual: CD only. Instead of moving in the Movement phase, any Chaos Character (with either no Mark of Chaos or a matching Mark of Chaos) can attempt to summon this unit. Roll up to 3D6, summoning the unit if the roll is equal to or greater than the Power Rating (within 12" of the summoner, and more than 9" from any enemies). On a double, the summoner takes a mortal wound. On a triple, the summoner takes D3 mortal wounds.
- On 2D6: 8.33% chance of successful summon; 16.66% chance of 1 Wound.
- On 3D6: 50% chance of successful summon; 41.66% chance of 1 Wound; 2.77% chance of D3 Wounds.
- Mark of Chaos ability: CD only. And these are very useful abilities!
- Khorne: Unstoppable Ferocity. +1 S and +1 A when charging, being charged, or performing a Heroic Intervention.
- Tzeentch: Ephemeral Form. Invulnerable save increased from 5+ to 4+.
- Nurgle: Disgustingly Resilient. 1 in 3 chance of ignoring each point of damage.
- Slaanesh: Quicksilver. Always fights first.
- Prince of Chaos: allows certain friendly units within 6" to re-roll to-hit rolls of 1. For HA, this is all <Legion> and <Mark> Daemon units. For CD, this is only <Mark> Daemon units.
- Psychic powers differ: HA uses Dark Hereticus whereas CD uses Nurgle/Slaanesh/Tzeentch as appropriate. Which powers you find most useful depends on your strategy. But do note that you can choose your psychic powers now (no need to roll on a random table).
- Faction: HA has Heretic Astartes and <Legion> (and is included on both the Thousand Sons and Death Guard unit list); CD has Daemon.
- Note that the HA Daemon Prince does get the "Chaos" keyword, but not as a faction; this means that a Nurgle Heretic Astartes Daemon Prince still counts for Epidemius's Tally of Pestilence, for example.
- Further note that the CD Daemon Prince has a "Daemon Prince of Chaos" keyword that should almost certainly be corrected to "Daemon Prince" in line with Be'lakor. Also Magnus the Red, for some reason, doesn't have the "Daemon Prince" keyword; probably an oversight.
Another factor to consider is what other units you have in your army that could potentially buff the Daemon Prince. The Chaos Daemons HQ models will happily work with either since they both have the Daemon keyword (even if it's not a Faction keyword for the HA version). But If you're using various Heretic Astartes HQ units, the bonuses they provide will only help a HA Daemon Prince.
Otherwise, given the combination of the difference in Wounds and the Mark of Chaos abilities, the Chaos Daemons version definitely has the edge. Disgustingly Resilient, for example, is broadly equivalent to a 50% uplift in wounds (it's actually worth slightly more due to a gearing effect of healing), so you're comparing HA's 8 against CD with effectively 15, for the same points cost!