My main guys rn are Herc, Musashi and Ishtar. So seeing the gacha rate ups this month had me thinking of having at least one support or maybe start an arts team. Now I'm torn between who I should get first, Jeanne or Tamamo. I'm also saving for Waver when he gets a solo rate up.
If you are going to roll this event I think you should go for Jeanne.
If they go by the JP schedule (and excluding class based summoning campaigns) Tamamo will have another rate up during the CCC pre-event in late April and then again another rate up in mid-June with the onigashima Rerun event.
Jeanne doesn't get one until November if they do the Apocrytha event.
Jeanne is not really that useful for Arts teams unless they are stall or crit-based. Even if you do use her on those types of teams, she is outclassed by another Arts servant that can cast defensive buffs/generate stars.
Tamamo is core to most Arts setups so if you have the Quartz now and really want her, you should roll for her instead.
In terms of availability, Jeanne doesn't get a solo rate up for a long time. Tamamo will get one come April/May.
In terms of gameplay...it depends on the team you want.
Jeanne is for STALL...which tends to be arts-based. (Mash, Jeanne, d'Eon, Georgios, Waver, Hans, Martha...these are all arts servants.) She's also much less resource intense than Tamamo...super easy to ascend and her mats aren't bad because you'd ideally want to keep her skills around 6/6/10. Her only material is hearts and we're about to get a good farming location for those.
Tamamo dramatically improves ANY arts team, but she really shines in dedicated NP spamming teams. Tamamo + Waver + Arts DPS is a tried-and-true comp. If you have an arts DPS (Bride, Saberlot, Squirtoria, Robin Hood, Vlad, Da Vinci, etc.), stick Tamamo and Waver on a team with them and have fun. But Tamamo needs an NP gain CE (preferably Prisma Cosmos, but something like Divine Banquet or her Bond CE works too) to be really effective. Skill levels matter in a Tamamo team since one of her biggest draws is reducing skill levels; therefore, you'd need to REALLY invest in leveling your servants' skills.
Stall also appreciates Tamamo. Jeanne + Tamamo + Mash/Waver = never dying. Ever.
The other issue with stall is that Tamamo + Waver + Arts DPS can, unless you're very unlucky, go through most matches without ever worrying about taking a hit from an NP. Tamamo has a targeted charge reduction and Waver has an AOE cooldown reduction on his very spammable (especially with Tamamo in play) np.
There's also the Arts Crit team...I guess you could stick Tamamo on one of those, but Caster Gil, Hans, Waver, and even Merlin feel like better supports because Tamamo has nothing in her kit around crit stars and if you give her 2030 her NP will go off a lot less than you'd like.
If you don't have either, Waver gets a rate-up in Chaldea Boys and Caster Gil's chance of showing up is essentially double since it's a boys-only banner.
tl;dr: Tamamo is more universally useful but requires more investment than Jeanne.
