NP4 Carmilla or NP1 Jack?

I think Jack is still just better, especially if you leveled her first skill for the 50% Quick card up. She gets all the stars, and her over charge effect last throughout the turn, rather than just for the NP attack. Jack also generates all the stars, and gets great NP gain off of her high hit counts. In addition, Jack removes buffs, and has an evade, both of which are great on her kit. The only thing Carmilla does that Jack doesn't is potentially remove charge, but even that is only up to an 80% chance at level 10.
Carmilla does work better with Merlin due to her buster NP, but as she'll only be brought in against Riders and Berserkers, the synergy is somewhat mitigated.
Jack overall is much more self sufficient than Carmilla, so I would stick with her.

As someone with lv90 10/10/6 Carmilla, all I can say is she destroys females and riders easily. Just give her np gain rate CE like magical girl sapphire and she will nuke them every 2 turns.

Jack is a better star generator, hands down, but Carmilla at NP4 is going to be the better boss killer. She can control the enemy NP gauge a bit while also healing herself on her NP. Ideally, you're using both of them to absolutely shred female bosses. And yeah, Carmilla is going synergize very well with Merlin.

My god! With an NP4 Carmilla and a good NP generating CE. She will definitely outpace and outdamage your Jack. As you've mentioned, she works well with Merlin which is another bonus for her.
Unless you get a NP2 Jack, go with Carmilla.

4* NP5 usualy surpasses NP1 5*. Which is why wellfares are so good.
Carmilla got a 20% attack up in her NP, who endures 3 turns.
With the right setup (Divine Banquet MLB, for example), she can spam it. And stack multiple attack-ups for a small time.

Since you have Merlin, she can get Mana Bust for 3 turns, and NP hit like a truck.