If we're just considering level 20 CE:
- Kaleidoscope
- +80% starting NP gauge
- +786 Attack
- Halloween Princess (fully ascended)
- +50% starting NP gauge
- +393 Attack / 589 HP (same stats as Prisma Cosmos and Moonlight Festival)
- +20% NP damage
So using the Halloween Princess (fully ascended) yields -393 Attack, -30% starting NP gauge, +589 HP, and +20% NP damage versus using Kaleidoscope.
With a level 20 Kaleidoscope, no buffs to NP or attack, and neutral attribute and class modifiers, your current Altera (assuming you have a level 1 NP, can't tell from your signature) will deal [13824*3*1.5*0.9*0.23] to [13824*3*1.5*1.1*0.23] damage to each target, or
12877 to 15738 damage to each target.
With a level 20 Halloween Princess, no buffs to NP or attack, and neutral attribute and class modifiers, your current Altera (assuming you have a level 1 NP, can't tell from your signature) will deal [13434*3*1.5*0.9*0.23*1.2] to [13434*3*1.5*1.1*0.23*1.2] damage to each target, or
15016 to 18353 damage to each target.
Difference in damage is about 2500/target. If you're fighting a single enemy then the Kaleidoscope is likely the better option since that damage is likely made up for with Altera's normal attacks. Against a wave of enemies then the Halloween Princess is likely the better choice.
Of the Servants you mentioned I would probably give the Halloween Princess to Emiya instead of Altera since Archers lose 5% of their total attack for damage purposes due to their class modifier (0.95x). Altera then would use Kaleidoscope.
Edit: One thing to keep in mind is that you can actually level your Halloween Princess up to 1000 Attack / 1500 HP, so eventually it would provide more raw damage than a level 20 Kaleidoscope. However that won't happen until well past level 50 I imagine, assuming a linear CE scale.